Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/extension-of-the-ahiezer-kac-determinant-formula-to-the-case-of-real-0W5tAZ0Its
References (47)
-
I. Gohberg, I. Felʹdman (1974)
Convolution Equations and Projection Methods for Their Solution -
S. Albeverio, K. Makarov (2001)
Ahiezer-Kac type Fredholm determinant asymptotics for convolution operators with rational symbolsTransactions of the American Mathematical Society, 353
-
S. Albeverio, K. Makarov (1997)
Nontrivial Attractors in a Model Related to the Three-Body Quantum ProblemActa Applicandae Mathematica, 48
-
G. Szegő (1920)
Beiträge zur Theorie der Toeplitzschen FormenMathematische Zeitschrift, 6
-
G. Baxter (1963)
A norm inequality for a “finite-section” Wiener-Hopf equationIllinois Journal of Mathematics, 7
-
R. Hartwig, M. Fisher (1969)
Asymptotic behavior of Toeplitz matrices and determinantsArchive for Rational Mechanics and Analysis, 32
-
(1966)
The continuous analogue of some theorems on Toeplitz matrices, Ukrain -
(1952)
On certain Hermitian forms associated with the Fourier series of a positive function, In: Festskrift Marcel Riesz -
A. Böttcher, B. Silbermann (1983)
Seminar Analysis 1982/1983 -
A. Böttcher, B. Silbermann (1991)
Analysis of Toeplitz Operators -
I. Hirschman (1966)
On a Formula of Kac and AchiezerIndiana University Mathematics Journal, 16
-
The continuous analogue of some theorems on Toeplitz matrices -
(1998)
The Efimov effect and an extended Szegö limit theorem,Lett -
M. E. Fisher, R. E. Hartwig (1968)
Toeplitz determinants: some applications, theorems, and conjecturesAdv. Chem. Phys., 15
-
B. M. McCoy, T. T. Wu (1973)
The Two-Dimensional Ising Model -
M. Kac (1954)
Toeplitz matrices, translation kernels and a related problem in probability theoryDuke Mathematical Journal, 21
-
I. Gohberg, S. Goldberg, M. Kaashoek (1990)
Classes of Linear Operators -
N. Nikol’skiĭ, N. Nikol’skiĭ (1986)
Treatise on the Shift Operator: Spectral Function Theory -
H. Widom (1975)
Asymptotic inversion of convolution operatorsPubl. Math. IHES, 44
-
I. Gohberg, M. Kaashoek, F. Schagen (1987)
Szegö-Kac-Achiezer formulas in terms of realizations of the symbolJournal of Functional Analysis, 74
-
G. Szegö (1915)
Ein Grenzwertsatz über die Toeplitzschen Determinanten einer reellen positiven FunktionMathematische Annalen, 76
-
H. Widom (1975)
Review: I. C. Gohberg and I. A. Fel′dman, Convolution equations and projection methods for their solutionBulletin of the American Mathematical Society, 81
-
M. Kac, W. Murdock, G. Szegő (1953)
On the Eigen-Values of Certain Hermitian FormsIndiana University Mathematics Journal, 2
-
M. Kac, W. L. Murdock, G. Szegö (1953)
On the eigenvalues of certain hermitian formsJ. Rational Mech. Anal., 2
-
J. MacCormick, B. Pavlov (1998)
A geometrical approach to calculating determinants of Wiener-Hopf operators, 504
-
(1983)
Wiener–Hopf determinants with symbols having zeros of analytic type,Seminar Analysis1982/1983 -
(1989)
Wiener–Hopf determinants with rational symbols, Math -
H. Dym, Shlomo Ta'assan (1981)
An abstract version of a limit theorem of SzegöJournal of Functional Analysis, 43
-
I. Gohberg, M. Kaashoek, S. Goldberg (1990)
Classes of Linear Operators Vol. I -
A. Böttcher (1989)
WIENER-HOPE Determinants with Rational Symbols†Mathematische Nachrichten, 144
-
A. Böttcher, B. Silbermann (1981)
The asymptotic behavior of Toeplitz determinants for generating functions with zeros of integral ordersMathematische Nachrichten, 102
-
(1986)
The asymptotic behavior of the determinants of truncated Wiener–Hopf operators in a singular case, Dokl -
S. Albeverio, S. Lakaev, K. Makarov (1998)
The Efimov Effect and an Extended Szegö–Kac Limit TheoremLetters in Mathematical Physics, 43
-
S. Albeverio, K. A. Makarov (1997)
Nontrivial attractors in a model related to the three-body problemActa Appl. Math., 48
-
Toeplitz Matrices (1975)
Toeplitz matrices generated by the Laurent series expansion of an arbitrary rational functionTransactions of the American Mathematical Society, 206
-
J. P. MacCormick, B. S. Pavlov (1996)
Irreversibility and Causality (Goslar -
H. Widom (1980)
Szegö's limit theorem: The higher-dimensional matrix case☆Journal of Functional Analysis, 39
-
(1965)
Introduction to the Theory of Linear Nonself-Adjoint Operators in Hilbert Space -
(1973)
Teoplitz determinants with singular generating functions, Amer -
I. I. Hirschman (1966)
On a formula of Kac and AhiezerJ. Math. Mech., 16
-
N. Nikol’skiĭ (1986)
Treatise on the Shift Operator -
H. Widom (1974)
Asymptotic inversion of convolution operatorsPublications Mathématiques de l'Institut des Hautes Études Scientifiques, 44
-
H. Widom (1973)
Toeplitz Determinants with Singular Generating FunctionsAmerican Journal of Mathematics, 95
-
(1986)
The asymptotic behavior of the determinants of truncated Wiener – Hopf operators in a singular case -
E. Basor (1978)
Asymptotic formulas for Toeplitz determinantsTransactions of the American Mathematical Society, 239
-
H. Widom (1985)
Asymptotic Expansions for Pseudodifferential Operators on Bounded Domains -
M. Krein, I. Gohberg (1969)
Introduction to the theory of linear nonselfadjoint operators
- Publisher
- Springer Journals
- Copyright
- Copyright © 2000 by Kluwer Academic Publishers
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1023/A:1006475727557
- Publisher site
- See Article on Publisher Site
Abstract
The Fredholm determinant asymptotics for self-adjoint convolution operators on finite intervals with real symbols vanishing on the real axis is studied. Explicit formulae are obtained in the case where the symbol satisfies the generalized zero index condition and has only two simple zeros of analytic type. These formulae are direct extensions of the Ahiezer–Kac–Szegö limit theorem which, in particular, take into account the oscillating character of the asymptotics.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 2, 2004