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REFERENCES

  1. R. Paley and N. Wiener,Fourier Transforms in the Complex Domain,Publ. Amer. Math. Soc., New York (1934).

    Google Scholar 

  2. N. Levinson,Gap and Density Theorems,Publ. Amer. Math. Soc., New York (1940).

    Google Scholar 

  3. B. Ya. Levin,Distribution o Zeros o Entire Functions [in Russian],GI L, Moscow (1956).

    Google Scholar 

  4. L. Schwartz,Etude des Sommes d'Exponentielles R éelles,Hermann, Paris (1943).

    Google Scholar 

  5. R. M. Redheffer,"Elementary remarks on completeness,"Duke Math. J.,35,103–116 (1968).

    Google Scholar 

  6. W. A. J. Luxemburg and J. Korevaar,"Entire functions and Müntz-Szász type approximation," Trans. Amer. Math. Soc.,157,23–37 (1971).

    Google Scholar 

  7. A. F. Leont'ev,Sequence o Polynomials in Exponentials[in Russian],Nauka, Moscow (1980).

    Google Scholar 

  8. A. M. Sedletskii,"π,π)," Trudy MEI,No. 146,167–174 (1972).

  9. R. M. Redheffer,"Completeness of sets of complex exponentials,"Adv. Math.,24,1–62 (1977).

    Google Scholar 

  10. H. J. Landau,"A sparse regular sequence of exponentials closed on large sets,"Bull. Amer. Math. Soc.,70,No. 4,566–569 (1964).

    Google Scholar 

  11. H. J. Landau,"On the completeness of a set of translates,"J. Approxim. Theory,5,No. 4,438–440 (1972).

    Google Scholar 

  12. M. F. Krasichkov-ernovskii,"On the absolute completeness of an exponential system on a closed interval,"Mat. Sb.,131,No. 3,309–322 (1986).

    Google Scholar 

  13. B. N. Khabibullin,"Completeness of sets of complex exponentials in convex sets,"In:Complex Analysis,Differential Equations,and Related Topics [in Russian],III,Ufa (2000),pp. 56–63.

  14. A. M. Sedletskii,"An analog of a Hardy-Littlewood theorem for Laplace transform and its applications,"Anal. Math.,11,343–354 (1985).

    Google Scholar 

  15. J. P. Kahane,"Sur la totalit é des suites d'exponentielles imaginaires,"Ann. Inst. Fourier(Grenoble), 8,273–275 (1959).

    Google Scholar 

  16. P. Koosis,"Sur latotalit é des systèmes d'exponentielles imaginaires,"C. R. Acad. Sci.,250,2102–2103 (1960).

    Google Scholar 

  17. P. Malliavin,On the Closure o a Sequence o Exponentials on a Segment,Lectures,Summer Insti-tute, Stanford Univ. (1961).

    Google Scholar 

  18. A. Beurling and P. Malliavin,"On the closure of characters and the zeros of entire functions,"Acta. Math.,118,79–93 (1967)

    Google Scholar 

  19. J. P. Kahane,Travaux de Beurlinget Malliavin,Benjamin, New York (1966).

    Google Scholar 

  20. R. M. Redheffer,"Two consequences of the Beurling-Malliavin theory,"Proc. Amer. Math. Soc., 36,116–122 (1972).

    Google Scholar 

  21. I. F. Krasichkov-Ternovskii,"An interpretation of the Beurling-Malliavin theorem on the completeness radius,"Mat. Sb.,180,No. 3,397–423 (1989).

    Google Scholar 

  22. A. Beurling and P. Malliavin,"On Fourier transforms of measures with compact support,"Acta. Math.,107,291–309 (1962).

    Google Scholar 

  23. B. N. Khabibullin,"Nonconstructive proofs of the Beurling-Malliavin theorem on the completeness radius and the nonuniqueness theorem for entire functions,"Izv. Ross. Akad. Nauk,Ser. Mat.,58, No. 4,125–148.(1994).

    Google Scholar 

  24. P. Koosis,Le çons sur le Th éorème de Beurlinget Malliaven,Les Publications CRM, Montr éal (1996).

    Google Scholar 

  25. E. Seneta, Regularly Varying Functions [Russian translation],Nauka, Moscow (1985).

  26. A. M. Sedletskii,"On the completeness and nonminimality of an exponential system in Lp (-π,π)," Sib. Mat. Zh.,29,No. 1,159–170 (1988).

    Google Scholar 

  27. A. I. Kheifets,"Characteristic of zeros of certain special classes of entire functions of nite degree," Teor. Funkts.,Funkts. Anal.,Pril. (Khar'kov),9,3–13 (1968).

    Google Scholar 

  28. R. M. Redhe.er and R. M. Young,"Completeness and basis properties of complex exponentials," Trans. Amer. Math. Soc.,277,93–111 (1983).

    Google Scholar 

  29. A. M. Sedletskii,"On the convergence of nonharmonic Fourier series with respect to exponential, sine,and cosine systems,"Dokl. Akad. Nauk SSSR,301,1053–1056 (1988).

    Google Scholar 

  30. E. I. Moiseev,"On the basis property of sine and cosine systems,"Dokl. Akad. Nauk SSSR,275, 794–798 (1984).

  31. A. N. Barmenkov,On Approximate Properties o Certain Function Systems,Thesis,MGU, Moscow (1984).

    Google Scholar 

  32. G. G. Devdariani,"On the basis property of a certain trigonometrical function system,"Differents. Uravn.,22,No. 1,168–170 (1986).

    Google Scholar 

  33. G. G. Devdariani,"On the basis property of a certain function system,"Differents. Uravn.,22, No. 1,170–171 (1986).

    Google Scholar 

  34. G. G. Devdariani,Basis Property o Certain Special Systems o Eigenfunctions o Non-Self-Adjoint Differential Operators,Thesis,MGU, Moscow (1986).

    Google Scholar 

  35. A. M. Sedletskii,"Spectral analysis of the differentiation operator,"In:Spectral and Evolution Problems,11,Proc. 11 Crimean Autumn Math. School-Symp.,September 2000,Sevastopol-Laspi, Simferopol (2001),pp. 8–18.

  36. S. G. Krein (Ed.),Functional Analysis [in Russian],Nauka, Moscow (1972).

    Google Scholar 

  37. A. M. Sedletskii,"Biorthogonal expansions of functions into exponential series on intervals of the real line,"Usp. Mat. Nauk,57,No. 5,51–95 (1982).

    Google Scholar 

  38. A. M. Sedletskii,"Approximate properties of exponential systems in L p (a,b),"Differents. Uravn., 31,No. 10,1639–1645 (1995).

    Google Scholar 

  39. A. M. Sedletskii,"Constructing complete,minimal,but not uniformly minimal exponential systems with a separable real spectrum in L p and C,"Mat. Zametki,58,No. 4,582–595 (1995).

    Google Scholar 

  40. V. A. Il'in,"Necessary and su.cient conditions for the basis property in L p and the equiconvergence with the trigonometrical series of spectral expansions and expansions in the exponential system," Dokl. Akad. Nauk SSSR,273,789–793 (1983).

    Google Scholar 

  41. A. I. Minkin,"Equiconvergence theorems for Differential operators,"In:Progress in Science and Technology,Series on Contemporary Mathematics and Its Applications,Thematical Surveys,49, Functional Analysis-4,All-Russian Institute for Scientific and Technical Information,Ross. Akad. Nauk, Moscow (1997).

    Google Scholar 

  42. R. J. Duffin and J. J. Eachus,"Some notes on an expansion theorem of Paley and Wiener,"Bull. Amer. Math. Soc.,48,No. 12,850–855 (1942).

    Google Scholar 

  43. V. D. Golovin,"On stability of an exponential function basis,"Dokl. Akad. Nauk ArmSSR,36, No. 2,65–70 (1963).

    Google Scholar 

  44. M. I. Kadets,"Exact value of the Paley-Wiener constant,"Dokl. Akad. Nauk SSSR,155,1253–1254 (1964).

    Google Scholar 

  45. R. J. Duffin and A. C. Schaeffer,"A class of nonharmonic Fourier series,"Trans. Amer. Math. Soc., 72,341–366 (1952).

    Google Scholar 

  46. A. M. Sedletskii,"Equivalent sequences in certain function spaces,"Izv. Vuzov,Mat.,No. 7,85–91 (1973).

  47. A. M. Sedletskii,"On the stability of Riesz bases in the spaces L 2 and H 2,"In:Inverse Problems for Differential Equations [in Russian],Novosibirsk (1972),pp. 157–163.

  48. B. Ya. Levin,"On exponential function bases in L 2,"Zap. Mat. Otd. Fiz.-Mat. Fak. KhGU i KhMO, Ser. 4,27,39–48 (1961).

    Google Scholar 

  49. B. Ya. Levin,"Interpolation by entire functions of exponential type,"In:Mathematical Physics and Functional Analysis [in Russian],F INT Akad. Nauk USSR,No. 1,Khar'kov (1969),pp. 136–146.

    Google Scholar 

  50. V. D. Golovin,"On biorthogonal expansions in linear combinations of exponential functions in L 2," Zap. Mekh.-Mat. Fac. KHGU i KhMO,Ser. 4,30,18–29 (1963).

    Google Scholar 

  51. V. Z. Katsnel'son,"On bases of exponential functions in L 2,"Funkts. Anal. Pril.,5,No. 1,37–47 (1971)

    Google Scholar 

  52. S. A. Avdonin,"On the problem on Riesz exponential bases in L 2,"Vestn. LGU,Ser. Mat.,Mekh., Astron.,13,No. 3,5–12 (1974).

    Google Scholar 

  53. B. S. Pavlov,"Basis property of the exponential system and the Muckenhoupt condition,"Dokl. Akad. Nauk SSSR,247,37–40 (1979).

    Google Scholar 

  54. G. M. Gubarev,"Spectral analysis of biorthogonal expansions into exponential series,"Izv. Akad. Nauk SSSR,Ser. Mat.,53,No. 6,1236–1268 (1989).

    Google Scholar 

  55. S. V. Khrushchev,"Perturbation theorems for exponential bases and the Mackenhoupt condition, Dokl. Akad. Nauk SSSR,247,44–48 (1979).

    Google Scholar 

  56. S. A. Avdonin and I. Joó,"Riesz bases of exponentials and sine-type functions,"Acta. Math. Hung., 51,3–14 (1988).

    Google Scholar 

  57. N. K. Nikol'skii,B. S. Pavlov,and S. V. Khrushchev,Unconditional Bases of Exponentials and ReproducingKernels,I [in Russian],Preprint LOMI R–8–80,Leningrad (1980).

  58. N. K. Nikol'skii,B. S. Pavlov,and S. V. Khrushchev,Unconditional Bases of Exponentials and ReproducingKernels,III [in Russian],Preprint LOMI R–10–80,Leningrad (1980).

  59. S. V. Hru ¢s ¯cev, N. K. Nikol'skii, and B. S. Pavlov,"Unconditional bases of exponentials and reproducing kernels,"Lect. Notes. Math.,864,214–335 (1981).

    Google Scholar 

  60. N. K. Nikol'skii,Lectures on the Shift Operator[in Russian],Nauka, Moscow (1980).

    Google Scholar 

  61. A. I. Minkin,"Reflections of exponents and unconditional exponential bases,"Algebra Analiz,3, No. 5,109–134 (1991).

    Google Scholar 

  62. N. K. Nikol'skii and B. S. Pavlov,"Bases of eigenvectors of completely non-unitary contractions and the characteristic function,"Izv. Akad. Nauk SSSR,Ser. Mat.,34,No. 1,90–133 (1970).

    Google Scholar 

  63. N. I. Akhiezer,Lectures on Approximation Theory [in Russian],Nauka, Moscow (1965).

    Google Scholar 

  64. Yu. I. Lyubarskii and K. Seip,"Sampling and interpolating sequences for multiband-limited functions and exponential bases on disconnected sets,"J. Fourier Anal. Appl.,3,No. 5,595–615 (1997).

    Google Scholar 

  65. K. Seip,"A simple construction of exponential bases in L 2 on the union of several intervals,"Proc. Edinburgh Math. Soc.,38,171–177 (1995).

    Google Scholar 

  66. Yu. I. Lyubarskii and I. Spitkovsky,"Sampling and interpolation for a lacunary spectrum,"Proc. Royal Soc. Edinburgh,126A,77–87 (1996).

    Google Scholar 

  67. A. Kohlenberg,"Exact interpolation of band-limited functions,"J. Appl. Phys.,24,1432–1436 (1953).

    Google Scholar 

  68. H. J. Landau,"Necessary density conditions for sampling and interpolation of certain entire functions,"Acta. Math,117,37–52 (1967).

    Google Scholar 

  69. L. Bezuglaja and V. E. Katsnelson,"The sampling theorem for functions with limited multi-band spectrum. I,"Z. Anal. Anwend.,12,511–534 (1993).

    Google Scholar 

  70. V. E. Katsnelson,"Sampling and interpolation for functions with multi-band spectrum:the mean periodic continuation method,"Z. Anal. Anwend.,15,91–132 (1996).

    Google Scholar 

  71. J.-L. Lions and E. Magenes,Inhomogeneous Boundary-Value Problems and Their Applications[Russian translation],Mir, Moscow (1971).

    Google Scholar 

  72. V. G. Maz'ya,S. L. Sobolev Spaces[in Russian],LGU, Leningrad (1985).

    Google Scholar 

  73. D. Russel,"On exponential bases for the Sobolev spaces over an interval,"J. Math. Anal. Appl., 87,528–550 (1982).

    Google Scholar 

  74. A. M. Sedletskii,"Approximate properties of exponential systems in Sobolev spaces,"Vestn. MGU, Ser. Mat.,Mekh.,No. 6,3–8 (1999).

  75. S. A. Avdonin and S. A. Ivanov,"Levin-Golovin theorem for Sobolev spaces,"Mat. Zametki,68, No. 2,163–172 (2000).

    Google Scholar 

  76. S. Ivanov and N. Kalton,"Interpolation of subspaces and applications to exponential bases,"Algebra Analiz,13,No. 2,93–115 (2001).

    Google Scholar 

  77. Yu. I. Lyubarskii and K. Seip,"Weighted Paley-Wiener spaces,"J. Fourier Anal. Appl. (in press).

  78. K.-D. Kürsten,"über zufällige Störungen einer Basis aus Exponentialfunktionen im Raum L2 [-π,π],"Z. Anal. Anwend. 1,31–36 (1982).

    Google Scholar 

  79. G. Chistyakov and Yu. Lyubarskii,"Random perturbations of exponential Riesz bases,"Ann. Inst. Fouri er,47,No. 1,205–255 (1997).

    Google Scholar 

  80. A. A. Shkalikov,"On properties of a part of eigen-and associated elements of self-adjoint quadratic operator pencils,"Dokl. Akad. Nauk SSSR,283,1100–1106 (1985).

    Google Scholar 

  81. S. I. Ponomarev,"On a certain eigenvalue problem,"Dokl. Akad. Nauk SSSR,249,2068–2070(1979).

    Google Scholar 

  82. A. M. Sedletskii,"Nonharmonic Fourier series,"In:Theory of Functions and Approximations,Proc. 4th Saratov Winter School,January 25-February 5,1988[in Russian],SGU, Saratov (1990),pp. 92–98.

    Google Scholar 

  83. G. G. Hardy, D. E. Littlewood, and G. Polya,Inequalities[in Russian]IL, Moscow (1948).

    Google Scholar 

  84. J. Elsner,"A,A),"Math. Z.,120,211–220 (1971).

    Google Scholar 

  85. W. O. Alexander (Jr.) and R. M. Redheffer,"The excess of sets of complex exponentials,"Duke Math. J.,34,59–72 (1967).

    Google Scholar 

  86. D. R. Peterson,"The excess of sets of complex exponentials,"Proc. Amer. Math. Soc.,44,321–325 (1974).

    Google Scholar 

  87. A. M. Sedletskii,"On completeness of the systems {exp(ix (n +ih n})),"Anal. Math.,4,125–143 (1978).

    Google Scholar 

  88. A. M. Sedletskii,"On pure imaginary perturbations of exponents ë n in the system {exp(ië n t})," Sib. Mat. Zh.,26,No. 4,151–158 (1985).

    Google Scholar 

  89. A. M. Sedletskii,"On the difference of excesses of two systems of exponential functions,"Trudy MEI,No. 357,98–102 (1978).

  90. A. M. Sedletskii,"Excesses of exponential function systems,"Mat. Zametki,22,No. 6,803–814 (1977).

    Google Scholar 

  91. A. M. Sedletskii,"Excesses of exponential function systems,"Izv. Akad. Nauk SSSR,Ser. Mat.,44, No. 1,203–218 (1980).

    Google Scholar 

  92. A. M. Sedletskii,"Excesses of close exponential systems in L p,"Sib. Mat. Zh.,24,No. 4,164–175 (1983).

    Google Scholar 

  93. A. M. Sedletskii,"Stability of classes of compactly supported Fourier transforms,"Integr. Preoobraz. Spets. Funktsii,Inform. Byul.,1,No. 2,17–19 (1997).

    Google Scholar 

  94. A. M. Sedletskii,"On entire functions of S. N. Bernshtein class that are not Fourier-Stieltjes transforms,"Mat. Zametki,61,No. 3,366–380 (1997).

    Google Scholar 

  95. A. M. Sedletskii,"Nonharmonic Fourier series,"Sib. Mat. Zh.,12,No. 5,1100–1114 (1971).

    Google Scholar 

  96. A. M. Sedletskii,"π,π),1 p 2," Trudy MEI,No. 290,63–69 (1976).

    Google Scholar 

  97. A. M. Sedletskii,"Analytic functions in the nonharmonic Fourier analysis,"Mat. Vestn.,40,315–320 (1988).

    Google Scholar 

  98. M. Yu. Yurkin,"Geometric conditions for minimality of exponential systems in L p [-π,π],"Mat. Zametki,58,No. 5,773–779 (1995).

    Google Scholar 

  99. A. M. Sedletskii,"On the stability of the uniform minimality of the exponential system,"In:Metrical Function Theory and Related Topics of Analysis[in Russian],A sF,Moscow (1999),pp. 221–237.

  100. R. Young,"π,π),"Proc. Amer. Math. Soc., 53,137–140 (1975).

    Google Scholar 

  101. A. M. Sedletskii,"On the completeness of the exponential system in spaces of Differential functions," Trudy MEI,No. 34,98–103 (1977).

    Google Scholar 

  102. A. F. Leont'ev,"Solution of a generalized convolution equation,"Izv. Akad. Nauk SSSR,Ser. Mat., 43,No. 2,342–366 (1979).

    Google Scholar 

  103. A. A. Shkalikov,"Strongly damped operator pencils and the solvability of the corresponding operator-Differential equations,"Mat. Sb.,135,No. 1,96–117 (1988).

    Google Scholar 

  104. E. I. Moiseev and A. P. Prudnikov,"On the basis property of systems of sines and cosines in the Sobolev spaces,"Bull. Pol. Acad. Sci.,Math.,44,No. 4,401–409 (1996).

    Google Scholar 

  105. A. M. Sedletskii,Fourier Transforms and Approximations,Gordon and Breach, Amsterdam (2000).

    Google Scholar 

  106. L. Schwartz,"Th éorie g énerale des fonctions moyenne-p ériodiques,"Ann. Math.,48,857–918 (1947).

    Google Scholar 

  107. A. F. Leont'ev,"On properties of sequences of Dirichlet polynomials converging on an interval of the imaginary axis,"Izv. Akad. Nauk SSSR,Ser. Mat.,29,No. 2,269–328 (1965).

    Google Scholar 

  108. A. F. Leont'ev,Exponential Series [in Russian],Nauka, Moscow (1976).

    Google Scholar 

  109. S. Verblunsky,"On an expansion in exponential series,"Quart. J. Math.,7,No. 27,231–240 (1956).

    Google Scholar 

  110. V. A. Molodenkov,"On expansions in eigenfunctions of a certain boundary-value problem,"In:Differential Equations and Computational Mathematics[in Russian],No. 2,SGU, Saratov (1975), pp. 56–65.

    Google Scholar 

  111. A. M. Sedletskii,"On functions periodic in the mean,"Izv. Akad. Nauk SSSR,Ser. Mat.,34,No. 6, 1388–1412 (1970).

    Google Scholar 

  112. A. M. Sedletskii,"On biorthogonal expansions in exponential functions,"Izv. Akad. Nauk SSSR, Ser. Mat.,36,No. 3,583–590 (1972).

    Google Scholar 

  113. V. A. Molodenkov,"M. Riesz equisummability of expansions in certain exponential function systems,"Mat. Zametki,15,No. 3,381–386 (1974).

    Google Scholar 

  114. A. M. Sedletskii,"On the equiconvergence and equisummability of nonharmonic Fourier expansions with ordinary Fourier series,"Mat. Zametki,18,No. 1,9–17 (1975).

    Google Scholar 

  115. A. M. Sedletskii,"On the uniform convergence of nonharmonic Fourier series,"Trudy Mat.Inst Akad. Nauk SSSR,200,299–309 (1991).

    Google Scholar 

  116. V. A. Molodenkov and A. P. Khromov,"Eigenfunction expansions of a certain boundary-value problem for the differentiation operator,"In:Differential Equations and Computational Mathematics[inRussian],No. 1,SGU, Saratov (1972),pp. 17–26.

    Google Scholar 

  117. A. M. Sedletskii,"Eigenfunction expansions of the differentiation operator with a spread boundary condition,"Differents. Uravn.,30,No. 1,70–76 (1994).

    Google Scholar 

  118. A. M. Sedletskii,"Exponential bases in the spaces L p,"Anal. Math.,8,215–232 (1982).

    Google Scholar 

  119. A. M. Sedletskii,"Periodic-in-mean extension and exponential function bases in L p (-π,π),"Mat. Zametki,12,No. 1,37–42 (1972).

    Google Scholar 

  120. A. M. Sedletskii,"Extension of the convergence of quasi-polynomials,"Izv. Akad. Nauk SSSR,Ser. Mat.,44,No. 5,1131–1149 (1980).

    Google Scholar 

  121. A. M. Sedletskii,"Periodic-in-mean extension of continuous functions with preservation of the smoothness,"Dokl. Akad. Nauk SSSR,212,302–304 (1973).

    Google Scholar 

  122. J.-P. Kahane,"Sur les fonctions moyenne-p ériodiques born ées,"Ann. Inst. Fourier,7,293–314 (1957).

    Google Scholar 

  123. V. D. Golovin,"On the generalization of the concept of periodic extension,"Dokl. Akad. Nauk SSSR,149,502–504 (1963).

    Google Scholar 

  124. J.-P. Kahane,"Sur quelques problèmes d'unicit é et de prolongement,"Ann. Inst. Fourier,5,39–130 (1953–54).

    Google Scholar 

  125. J. Delsarte,"Les fonctions'moyenne-p ériodiques',"J. Math. Pures Appl.,14,403–453 (1935).

    Google Scholar 

  126. A. M. Sedletskii,"On the solvability of a certain integral equation with an initial condition,"Differents. Uravn.,11,No. 12,2283–2285 (1975).

    Google Scholar 

  127. Yu. I. Lyubich,"On eigenfunctions and associated functions of the differentiation operator,"Izv. Vuzov,Mat.,No. 4,94–103 (1959).

  128. G. I. Gubarev,"On periodic-in-mean extensions of functions,"Funkts. Anal. Pril.,20,No. 1,67–68 (1986).

    Google Scholar 

  129. A. M. Sedletskii,"Extension of the convergence of quasi-polynomials and its application,"In:Studies in Complex Analysis [in Russian],BF Akad. Nauk SSSR,UFA (1987),pp. 144–158.

    Google Scholar 

  130. J. Hale,Theory of Functional-Differential Equations[Russian translation],Mir, Moscow (1984).

    Google Scholar 

  131. A. M. Sedletskii,"Backward continuation of solutions to a homogeneous convolution equation of retarded type,"Differents. Uravn.,27,No. 4,709–711 (1991).

    Google Scholar 

  132. S. A. Nefedov,"On dynamical systems with a nonexpanding attainability domain,"Differents. Uravn.,16,No. 11,1995–2002 (1980).

    Google Scholar 

  133. S. A. Nefedov,On Controllability o Linear Infinite-Dimensional Systems,Thesis,UrGU, Sverdlovsk (1981).

    Google Scholar 

  134. A. M. Sedletskii,"Exponential function expansions,"Sib. Mat. Zh.,16,No. 4,820–829 (1975).

    Google Scholar 

  135. A. M. Sedletskii,"On summability and convergence of nonharmonic Fourier series,"Izv. Ross. Akad. Nauk,Ser. Mat.,64,No. 3,151–168 (2000).

    Google Scholar 

  136. A. M. Sedletskii,"Bases arising in solving mixed-type equations,"Differents. Uravn. 35,No. 4, 507–515 (1999).

    Google Scholar 

  137. I. Stein,Singular Integrals and Differential Properties o Functions[Russian translation],Mir, Moscow (1973).

    Google Scholar 

  138. R. M. Young,An Introduction to Nonharmonic Fourier Series,Academic Press, New York (1980).

    Google Scholar 

  139. Yu. I. Lyubich,"On a certain class of integral equations,"Mat. Sb.,38,No. 2,183–202 (1956).

    Google Scholar 

  140. S. Verblunsky,"On a class of integral functions,"Quart. J. Math.,8,No. 32,312–320 (1957).

    Google Scholar 

  141. A. M. Sedletskii,"On a certain class of biorthogonal expansions in exponential functions,"Izv. Akad. Nauk SSSR,Ser. Mat. 41,No. 2,393–415 (1977).

    Google Scholar 

  142. R. Bellman and K. Cooke,Differential-Difference Equations [Russian translation],Mir, Moscow (1967).

    Google Scholar 

  143. A. M. Sedletskii,"On a certain class of nonharmonic Fourier series,"In:Certain Problems o Mathematics in Problems o Physics,Mechanics,and Economics [in Russian],MFTI, Moscow (1990), pp. 112–117.

    Google Scholar 

  144. A. M. Sedletskii,"Homogeneous convolution equations of retarded type. Backward continuation. Applications to nonharmonic Fourier series,"In:Linear Operators in Complex Analysis [in Russian], RGU, Rostov-on-Don (1994),pp. 81–87.

    Google Scholar 

  145. I. A. Baigusheva,Expansions o Solutions to a Homogeneous Differential-Difference Equation of Retarded Type into Series in Exponential Solutions [in Russian],Thesis,MGU, Moscow (1998).

    Google Scholar 

  146. A. V. Skokov,"On biorthogonal expansion of integrable functions into exponential series,"Vest n. MEI,No. 4,89–94 (1994).

  147. A. M. Sedletskii,"Nonharmonic Fourier series without the Riemann-Lebesgue property,"Izv. Ross. Akad. Nauk,Ser. Mat.,58,No. 6,123–136 (1994).

    Google Scholar 

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Sedletskii, A.M. Nonharmonic Analysis. Journal of Mathematical Sciences 116, 3551–3619 (2003). https://doi.org/10.1023/A:1024107924340

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