This is a preview of subscription content, log in via an institution to check access.
Bibliography
Achiezer, N.I.,The continuous analogues of some theorems on Toeplitz matrices, Ukrainian Math. J16 (1964), 445–462.
Baxter, G.,A convergence equivalence related to polynomials on the unit circle, Trans. Amer. Math. Soc.99 (1961), 471–487.
Baxter, G.,A norm inequality for a finite ‘section’ Wiener-Hopf equation, Illinois Jour. Math.7 (1963), 97–103.
Böttcher, A and Silbermann, B,The asymptotic behaviour of Toeplitz determinants for generating functions with zeros of integral orders, Math. Nachr.102 (1981), 79–105.
Böttcher, A and Silbermann, B, “Invertibility and asymptotics of Toeplitz matrices. Math. Forschung 17,” Akademie-Verlag, 1983.
Carey, R.W. and Pincus, J.D.,Joint Torsion, Preprint (1995–1996), 1–174.
Carey, R.W. and Pincus, J.D.,Joint Torsion of Toeplitz operators with H ∞ symbols, Integral Equations and Operator Theory (1998), 1–32 to appear.
Carey, R. and Pincus, J,Mosaics, Principal functions and mean motion in von Neumann algebras, Acta Mathematica138 (1977), 153–218.
Deutsch, F.,The alternating method of von Neumann, Internat. Ser. Numer. Math., Multivariate approximation theory, Proc. conf. Math. Res. Institute. Oberwolfach51, 83–96 (1977), Birkhauser Verlag, Basel-Boston.
Gohberg, I.C. and Fel'dman, I.A., “Convolution equations and projection methods for their solution,” American Mathematical Society; Trans. of Math. Monographs Volume 41, 1974 from the Russian 1971.
Gohberg, I. and Levcenko, V.I., Math. Issled6:4 (1971) 20–36.
Gohberg, I. and Prössdorf S.,Ein Projektionsverfarhen zur Lösung entarteter Systeme von diskreten Wiener-Hopf-Gleichungen, Math. Nachr.65 (1975), 19–45.
Grenander, U. and Szegö, F, “Toeplitz forms and their applications,” Univ. of California Press, 1957.
Kac, M.,Toeplitz matrices, translation kernels and a related problem in probability, Duke Math. J.21 (1954), 501–509.
Kac, M., Murock, W. and Szegö, G.,On the eigenvalues of certain hermitian forms, J. Rational Mechanics and Analysis2 (1953), 767–800.
Knudsen, F.F. and Mumford, D.,The projectivity of the moduli space of stable curves. I; preliminaries on “Det” and “Div”, Math. Scand.39 (1976), 19–55.
Krein, M.G.,On some investigations in the perturbation theory of self-adjoint operators (Russian), First Summer School, Kiev (1964), 103–187.
Linnik, I. Ju,A multidimensional analogue of the a limit theorem of G. Szegö, Math USSR-Izvestia9 (1975), 1323–1332.
Nikol'skii, N.K., “Treatise on the shift operator,” Springer-Verlag, Grundlehren 273, Berlin, 1986.
Peller, V.,Functional calculus for a pair of commuting self-adjoint operators, J. Funct. Anal.112 (1993), 325–342.
Pietsch, A., “Eigenvalues and s-numbers,” Cambridge University Press- Studies in Advanced Mathematics #13, 1987.
Pincus, J.D. Editor, Summer Institute on Spectral Theory and Statistical Mechanics (1965), Brookhaven National Laboratory, Upton N.Y.
Quillen, D.G.,Det of Cauchy Riemann Operators on Riemann Surfaces, Functional Analysis Appl (1985), 31–34.
Ramakrishnan, D.,Regulators, Algebraic cycles, Values of L-functions, Contemporary Math. “Algebraic K-Theory and Algebraic Number Theory”83 (1989).
Riesz, F. and Sz.-Nagy, B., “Lecons D'analyse Fonctionnelle, 2'nd ed.,” Akademie Kiado, Budapest, 1953.
Szegö, G,Ein Grenzwertsatz über die Toeplitzschen Determinanten einer reelen positiven function, Math. Ann,76 (1915), 490–503.
Szegö, G,on certain Hermitian forms associated with the fourier series of a positive function, Festskrift Marcel Riesz (Lund 1952), 228–238.
Sz-Nagy and C. Foias, “Analyse Harmonique Des Operateurs de L'espace de Hilbert,” Masson et Cie, 1967.
Vasyunin, V.I.,Unconditionally convergent spectral expansions and interpolation problems, Trudy. Mat. Inst. Steklov, [Russian]130 (1977), 5–49.
Widom, H.,Szegö's limit theorem: The higher dimensional matrix case, Jour. Funct. Analysis39 (1980), 182–198.
Widom, H., “Asymptotic Expansions for Pseudodifferential Operators on Bounded Domains,” Springer-Verlag, Lecture Notes in Mathematics 1152.
Kolmogorov, A.N. and Rozanov, Yu.A., On conditions for strong mixing of a stationary Gaussian process, Teor. Verojatnost. i. Primen5 (1960), 221–227.
Helson, H. and Szegö, G.,A problem of prediction theory, Ann. Mat. Pura Appl.51 (1960), 107–138.
Helson, H. and Sarason, D.,Past and Future, Math. Scand.21 (1967), 5–16.
J. Anderson and L.N. Vaserstein,Commutators in ideals of trace class operators, Indiana Univ. Math. Jour.35 (1986), 345–372.
D. Quillen, “Actes Congress Intern. Math.-Cohomology of Groups”, 1970.
Orth., D.,The discrete Wiener-Hopf equation, Math. Ann.182 (1969), 104–120.
I.A. Volodin,Algebraic K-theory as an extraordinary homology theory on the category of associative rings with 1, Isz. AN. USSR, Ser mat35 (1971), 844–873.
Devinatz, A.,The strong Szegö limit theorem, Illinois. J. Math11 (1967), 160–175.
Widom, H,Asymptotic behavior of block Toeplitz matrices and determinants, II, Adv. in Math.21 (1976), 1–29.
Fisher, M.E. and Hartwig R.E.,Toeplitz determinants, some applications, theorems and conjectures, Adv. Chem. Phys.15 (1968), 333–353.
Fisher, M.E. and Hartwig R.E.,Asymptotic behavior of Toeplitz matrices and determinants, Arch. Rat. Mech. Anal.32 (1969), 190–255.
J. Silvester, “Introduction to Algebraic K-Theory”, Chapman and Hall, New York, 1981.
Berrick, A.J., “An approach to algebraic K-theory”, Pitman Notes in Math. London, 1982.
T.T. Wu,Theory of Toeplitz determinants and spin correlations of the two dimensional Ising model, Physical Review149 (1996), 380.
Fisher, M.E. and Stephenson, J.,Statistical mechanics of dimers on a plane lattice, II, Dimer correlations and monomers, Physical Review132 (1963), 1411–14341.
Lenard, A.,Momentum distribution in the ground state of the one dimensional system of impenetrable bosons, J. Math, Phys.5 (1964), 930–943.
Lenard, A.,Some remarks on large Toeplitz determinants, Pacific Jour. Math.42 (1972), 137–145.
Dyson, F.,Statistical theory of the energy levels of complex systems, I, J. Math., Phys.3 (1962), 140.
Dyson, F.,A Brownian motion model for the eigenvalues of a random matrix, III, J. Math,. Phys.3 (1962), 1191.
Wilson, K.,Proof of a conjecture of Dyson, J. Math, Phys.3, 1040.
Hayashi, E.,The kernel of a Toeplitz operator, Integral Equations and Operator Theory9 (1986), 588–591.
Malmquist, F.,Sur la détermination d'une class de fonctions analytiques par leurs valeurs dans un ensemble donné de points, Comptes Rendues du Sixième Congrès (1925) des mathématiciens scandinaves (Koppenhagen, 1926), 253–259.
Walsh, J.L., “Interpolation and approximation by rational functions in the complex domain”, Amer. Math. Soc Colloquium Publications. vol 20, 1935.
Bass, H., “Algebraic K-Theory” W.A. Benjamin, N.Y., 1968.
Author information
Authors and Affiliations
Additional information
This work has been supported by National Science Foundation grants.