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References
J. L. Abreu, “A note on harmonizable and stationary sequences,” Bol. Soc. Mat. Mexicana 15(1970), 48–51.
R. G. Bartle, “A general bilinear vector integral,” Studia Math. 15(1956), 337–352.
R. C. Blei, “An elementary proof of the Grothendieck inequality,” Proc. Amer. Math. Soc. 100(1987), 58–60.
S. Bochner, “Stationarity, boundedness, almost periodicity of random valued functions,” Proc. Third Berkeley Symp. Math. Statist. & Prob. 2(1956), 7–27.
J. Calbrix, “Mesures non σ-finies: désintegration et quelques autres proprietés,” Ann. Inst. H. Poincaré 17(1981), 75–95.
S. Cambanis, “Complex symmetric stable variables and processes,” in: Contributions to Statistics, North-Holland, Amsterdam, 1983, 63–79.
D. K. Chang and Rao, M. M., “Bimeasures and nonstationary processes,” in: Real and Stochastic Analysis, Wiley, New York, 1986, 7–118.
_____, “Special representations of weakly harmonizable processes,” Stochastic Anal. Appl. 6(1988), 169–189.
S. D. Chatterji, “Orthogonally scattered dilation of Hilbert space valued set functions,” in: Measure Theory Proceedings, Lect. Notes in Math. No. 945, Springer-Verlag, 1982, 269–281.
M. Cotlar and Sadosky, C., “Majorized Toeplitz forms and weighted inequalities with general norms,” in Lect. Notes in Math. No. 908, Springer-Verlag, 1982, 139–168.
H. Cramér, “A contribution to the theory of stochastic processes,” Proc. Second Berkeley Symp. Math. Statist. & Prob. 1951, 329–339.
N. Dinculeanu, Vector Measures, Pargamon Press, London, 1967.
I. Dobrakov, “On integration in Banach spaces-VIII,” Čzech Math. J. 37(1987), 487–506.
N. Dunford and Schwartz, J. T., Linear Operators, Part I: General Theory, Wiley-Interscience, New York, 1958.
D. A. Edwards,” “Vector-valued measure and bounded variation in Hilbert space,” Math. Scand. 3(1955), 90–96.
P. Eymard, “L'algèbre de Fourier d'un groupe localement compact,” Bull. Soc. Math. France 92(1964), 181–236.
M. Fréchet, “Sur les fonctionnelles bilineares,” Trans. Amer. Math. Soc. 16(1915), 215–254.
J. E. Gilbert and Leih, T. J., “Factorization, tensor products, and bilinear forms in Banach space theory,” in: Notes in Banach Spaces, Univ. of Texas Press, Austin, 1980, 182–305.
J. E. Gilbert, Ito, T., and Schreiber, B. M., “Bimeasure algebras on locally compact groups,” J. Functional Anal. 64(1985), 134–162.
C. C. Graham and Schreiber, B. M., “Bimeasure algebras on LCA groups,” Pacific J. Math. 115(1984), 91–127.
_____, “Sets of interpolation for Fourier transforms of bimeasures,” Colloq. Math. 51(1987), 149–154.
_____, “Projections in spaces of bimeasures,” Canad. Math. Bull., to appear.
E. Hewitt and Ross, K. A., Abstract Harmonic Analysis — I, Springer-Verlag, New York, 1963.
_____, Abstract Harmonic Analysis — II, Springer-Verlag, New York, 1970.
H. Heyer, “Probability theory on hypergroups: a survey,” in: Probability Measures on Groups VII, Lect. Notes in Math. No. 1064, Springer-Verlag, New York, 1984, 481–550.
J. Horowitz, “Une remarque sur le bimesures,” in: Sem. Prob. XI, Lect. Notes in Math. No. 581, Springer-Verlag, New York, 1977, 59–64.
Y. Hosoya, “Harmonizable stable processes,” Z. Wahrs. 60(1982), 517–533.
R. I. Jewett, “Spaces with an abstract convolution of measures,” Adv. Math. 18(1975), 1–101.
Y. Kakihara, “A note on harmonizable and V-bounded processes,” J. Multivar. Anal. 16(1985), 140–156.
_____, “Strongly and weakly harmonizable stochastic processes of H-valued random variables,” J. Multivar. Anal. 18(1986), 127–137.
K. Karhunen, “Über lineare Methoden in der Wahrscheinlichkeitsrechnung,” Ann. Acad. Sci. Fenn, Ser AI Math. 37(1947), 3–79.
I. Kluvanek, “Remarks on bimeasures,” Proc. Amer. Math. Soc. 81(1981), 233–239.
J. Kuelbs, “A representation theorem for symmetric stable processes and stable measures on H,” Z. Wahrs. 26(1973), 259–271.
R. Lasser, “Orthogonal polynomials and hypergroups,” Rend. Math., Ser. 7 3(1983), 185–208.
_____, “Convolution semigroups on hypergroups,” Pacific J. Math. 127(1987), 353–371.
R. Lasser and Leitner, M., “Stochastic processes indexed by hypergroups,” J. Theoretical Prob., to appear.
P. Lévy, “Sur les fonctionnelles bilineares,” C. R. Acad. Sci., Paris, Ser I, Math. 222(1946), 125–127.
R. I. Loebl, “A Hahn decomposition for linear maps,” Pacific J. Math. 65(1976), 119–133.
Loève, M., “Fonctions aléatories du second ordres,” Note in P. Lévy's Processes Stochastiques et Movement Brownien, Gauthier-Villars, Paris, 1947, 228–352.
A. Makagon and Salehi, H., “Spectral dilation of operator-valued measures and its application to infinite dimensional harmonizable processes,” Studia Math. 85(1987), 257–297.
M. B. Marcus, “ξ-radial processes and random Fourier series,” Mem. Amer. Math. Soc. 368(1987), 181pp.
F. I. Mautner, “Unitary representations of locally compact groups — II,” Ann. Math. 52(1950), 528–556.
_____, “Note on Fourier inversion formula on groups,” Trans. Amer. Math. Soc. 78(1955), 371–384.
E. Merzbach and Zakai, M., “Bimeasures and measures induced by planar stochastic integrators,” J. Multivar. Anal. 19(1986), 67–87.
M. Morse and Transue, W., “Functions of bounded Fréchet variation,” Canad. J. Math. 1(1949), 153–165.
_____, “ℂ-bimeasures Λ and their superior integrals Λ*,” Rend. Circolo Mat. Palermo 4(1955), 270–300.
_____, “ℂ-bimeasures Λ and their integral extensions,” Ann. Math. 64(1956), 480–504.
_____, “The representation of a ℂ-bimeasure on a general rectangle,” Proc. Nat. Acad. Sci., USA 42(1956), 89–95.
M. A. Naimark, Normed Rings, Noordhoff, Groningen, 2d edition (translation), 1964.
H. Niemi, “Stochastic processes as Fourier transforms of stochastic measures,” Ann. Acad. Sci. Fenn, Ser AI Math. 591(1975), 1–47.
_____, “On orthogonally scattered dilations of bounded vector measures,” Ann. Acad. Sci. Fenn, Ser AI Math. 3(1977), 43–52.
Y. Okazaki, “Wiener integral by stable random measure,” Mem. Fac. Sci. Kyushu Univ., Ser A Math. 33(1979), 1–70.
G. Pisier, “Factorization of Linear Operators and Geometry of Banach Spaces, CMBS Monograph No. 60, Amer. Math. Soc., Providence, 1986.
M. Pourahmadi, “On minimality and interpolation of harmonizable stable processes,” SIAM J. Appl. Math. 44(1984), 1023–1030.
B. S. Rajput and Rama-Murthy, K., “Spectral representation of semistable processes and semistable laws on Banach spaces,” J. Multivar. Anal. 21(1987), 139–157.
M. M. Rao, “Extensions of the Hausdorff-Young theorem,” Israel J. Math. 6(1968), 133–149.
_____, “Compact operators and tensor products,” Bull. Acad. Pol. Sci. 23(1975), 1175–1179.
_____, “Covariance analysis of nonstationary times series,” in: Developments in Statistics — I, Academic Press, New York, 1978, 171–225.
_____, “Harmonizable processes: structure theory,” L'Enseign. Math. 28(1982), 295–351.
_____, “Harmonizable signal extraction, filtering, and sampling,” in: Topics in Non-Gaussian Signal Processes, Springer-Verlag, New York, 1989, 98–117.
_____, “Harmonizable Cramér, and Karhunen classes of processes,” Handbook of Statistics, Vol. 5, North-Holland, Amsterdam, 1985, 279–310.
M. Rosenberg, “Quasi-isometric dilation of operator valued measures and Grothendieck's inequality,” Pacific J. Math. 103(1982), 135–161.
J. Rosinski, “On stochastic integral representations of stable processes with sample paths in Banach spaces,” J. Multivar. Anal. 20(1986), 277–302.
Yu. A. Rozanov, “Spectral analysis of abstract functions,” Theor. Prob. Appl. 4(1959), 271–287.
_____, Stationary Random Processes, Holden-Day, Inc., San Francisco, 1967 (translation).
M. Schilder, “Some structure theorems for the symmetric stable laws,” Ann. Math. Statist. 41(1970), 412–421.
I. E. Segal, “An extension of Plancherel's formula to separable unimodular groups,” Ann. Math. 52(1950), 272–292.
_____, “Decomposition of operator algebras-I,” Mem. Amer. Math. Soc. 9(1951), 67 pp.
Ya. G. Sinai, “On properties of spectra of ergodic dynamical systems,” Dokl. Acad. Nauk USSR 150(1963), 1235–1237.
R. Spector, “Mesures invariantes sur les hypergroupes,” Trans. Amer. Math. Soc. 239(1978), 147–165.
N. Tatsuuma, “A duality theorem for locally compact groups,” J. Math. Kyoto Univ. 6(1967), 187–293.
K. Urbanik, “Random measures and harmonizable sequences,” Studia Math. 31(1968), 61–88.
N. Th. Voropoulos, “Tensor algebras and harmonic analysis,” Acta Math. 119(1967), 51–112.
R. C. Vrem, “Harmonic analysis on compact hypergroups,” Pacific J. Math. 85(1979), 239–251.
_____, “Idempotent sets and lacunarity for hypergroups,” preprint.
A. Weron, “Harmonizable stable processes on groups: spectral, ergodic, and interpolation properties,” Z. Wahrs. 68(1985), 473–491.
A. M. Yaglom, “Positive definite functions and homogeneous random fields on groups and homogeneous spaces,” Soviet Math. 1(1960), 1402–1405.
_____, “Second order homogeneous random fields,” Proc. Fourth Berkeley Symp. Math. Statist. & Prob. 2(1961), 593–622.
K. Ylinen, “Fourier transforms of noncommutative analogs of vector measures and bimeasures with applications to stochastic processes,” Ann. Acad. Sci. Fenn, Ser AI Math. 1(1975), 355–385.
_____, “On vector bimeasures,” Ann. Mat. Pura Appl. 117(1978), 115–138.
_____, “Dilations of V-bounded stochastic processes indexed by a locally compact group,” Proc. Amer. Math. Soc. 90(1984), 378–380.
_____, “Random fields on noncommutative locally compact groups,” in: Probability Measures On Groups — VIII, Notes in Math. No. 1210, Springer-Verlag, New York, 1986, 365–386.
_____, “Noncommutative Fourier transformations of bounded bilinear forms and completely bounded multilinear operators,” (UCR Tech. Report No. 12), 1987, J. Functional Anal., to appear.
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Rao, M.M. (1989). Bimeasures and harmonizable processes (Analysis, classification, and representation). In: Heyer, H. (eds) Probability Measures on Groups IX. Lecture Notes in Mathematics, vol 1379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087858
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