The Experts below are selected from a list of 411 Experts worldwide ranked by ideXlab platform
Skrettingland Eirik - One of the best experts on this subject based on the ideXlab platform.
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A Wiener Tauberian theorem for operators and Functions
2020Co-Authors: Luef Franz, Skrettingland EirikAbstract:We prove variants of Wiener's Tauberian theorem in the framework of quantum harmonic analysis, i.e. for convolutions between an Absolutely Integrable Function and a trace class operator, or of two trace class operators. Our results include Wiener's Tauberian theorem as a special case. Applications of our Tauberian theorems are related to localization operators, Toeplitz operators, isomorphism theorems between Bargmann-Fock spaces and quantization schemes with consequences for Shubin's pseudodifferential operator calculus and Born-Jordan quantization. Based on the links between localization operators and Tauberian theorems we note that the analogue of Pitt's Tauberian theorem in our setting implies compactness results for Toeplitz operators in terms of the Berezin transform. In addition, we extend the results on Toeplitz operators to other reproducing kernel Hilbert spaces induced by the short-time Fourier transform, known as Gabor spaces. Finally, we establish the equivalence of Wiener's Tauberian theorem and the condition in the characterization of compactness of localization operators due to Fern\'andez and Galbis.Comment: 39 page
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A Wiener Tauberian theorem for operators and Functions
2020Co-Authors: Luef Franz, Skrettingland EirikAbstract:We prove variants of Wiener's Tauberian theorem in the framework of quantum harmonic analysis, i.e. for convolutions between an Absolutely Integrable Function and a trace class operator, or of two trace class operators. Our results include Wiener's Tauberian theorem as a special case. Applications of our Tauberian theorems are related to localization operators, Toeplitz operators, isomorphism theorems between Bargmann-Fock spaces and quantization schemes with consequences for Shubin's pseudodifferential operator calculus and Born-Jordan quantization. Based on the links between localization operators and Tauberian theorems we note that the analogue of Pitt's Tauberian theorem in our setting implies compactness results for Toeplitz operators in terms of the Berezin transform. In addition, we extend the results on Toeplitz operators to other reproducing kernel Hilbert spaces induced by the short-time Fourier transform, known as Gabor spaces. Finally, we establish the equivalence of Wiener's Tauberian theorem and the condition in the characterization of compactness of localization operators due to Fern\'andez and Galbis.Comment: 39 pages v2) Accepted for publication in Journal of Functional Analysis. Smaller changes and references added based on helpful feedback from refere
Stan Hurn - One of the best experts on this subject based on the ideXlab platform.
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Modeling Structural Change in Money Demand Using a Fourier-Series Approximation
2007Co-Authors: Ralf Becker, Walter Enders, Stan HurnAbstract:The paper develops a simple method that can be used to test for a time-varying intercept and to approximate its form. The test is solidly grounded in asymptotic theory and has good small-sample properties. The methodology is based on the fact that a Fourier approximation can capture the variation in any Absolutely Integrable Function of time. As such, it is possible to use successive applications of the test to `back-out" the form of the time-varying intercept. We illustrate the methodology using an extended example concerning the demand for money
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Modelling Structural Change in Money Demand Using a Fourier-Series Approximation
2025Co-Authors: Ralf Becker, Walter Enders, Stan HurnAbstract:The paper develops a simple method that can be used to test for a time-varying intercept and to approximate its form. The test is solidly grounded in asymptotic theory and has good small-sample properties. The methodology is based on the fact that a Fourier approximation can capture the variation in any Absolutely Integrable Function of time. As such, it is possible to use successive applications of the test to "back-out" the form of the time-varying intercept. We illustrate the methodology using an extended example concerning the demand for money.structural break; fourier approximations; money demand
Luef Franz - One of the best experts on this subject based on the ideXlab platform.
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A Wiener Tauberian theorem for operators and Functions
2020Co-Authors: Luef Franz, Skrettingland EirikAbstract:We prove variants of Wiener's Tauberian theorem in the framework of quantum harmonic analysis, i.e. for convolutions between an Absolutely Integrable Function and a trace class operator, or of two trace class operators. Our results include Wiener's Tauberian theorem as a special case. Applications of our Tauberian theorems are related to localization operators, Toeplitz operators, isomorphism theorems between Bargmann-Fock spaces and quantization schemes with consequences for Shubin's pseudodifferential operator calculus and Born-Jordan quantization. Based on the links between localization operators and Tauberian theorems we note that the analogue of Pitt's Tauberian theorem in our setting implies compactness results for Toeplitz operators in terms of the Berezin transform. In addition, we extend the results on Toeplitz operators to other reproducing kernel Hilbert spaces induced by the short-time Fourier transform, known as Gabor spaces. Finally, we establish the equivalence of Wiener's Tauberian theorem and the condition in the characterization of compactness of localization operators due to Fern\'andez and Galbis.Comment: 39 page
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A Wiener Tauberian theorem for operators and Functions
2020Co-Authors: Luef Franz, Skrettingland EirikAbstract:We prove variants of Wiener's Tauberian theorem in the framework of quantum harmonic analysis, i.e. for convolutions between an Absolutely Integrable Function and a trace class operator, or of two trace class operators. Our results include Wiener's Tauberian theorem as a special case. Applications of our Tauberian theorems are related to localization operators, Toeplitz operators, isomorphism theorems between Bargmann-Fock spaces and quantization schemes with consequences for Shubin's pseudodifferential operator calculus and Born-Jordan quantization. Based on the links between localization operators and Tauberian theorems we note that the analogue of Pitt's Tauberian theorem in our setting implies compactness results for Toeplitz operators in terms of the Berezin transform. In addition, we extend the results on Toeplitz operators to other reproducing kernel Hilbert spaces induced by the short-time Fourier transform, known as Gabor spaces. Finally, we establish the equivalence of Wiener's Tauberian theorem and the condition in the characterization of compactness of localization operators due to Fern\'andez and Galbis.Comment: 39 pages v2) Accepted for publication in Journal of Functional Analysis. Smaller changes and references added based on helpful feedback from refere
Ralf Becker - One of the best experts on this subject based on the ideXlab platform.
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Modeling Structural Change in Money Demand Using a Fourier-Series Approximation
2007Co-Authors: Ralf Becker, Walter Enders, Stan HurnAbstract:The paper develops a simple method that can be used to test for a time-varying intercept and to approximate its form. The test is solidly grounded in asymptotic theory and has good small-sample properties. The methodology is based on the fact that a Fourier approximation can capture the variation in any Absolutely Integrable Function of time. As such, it is possible to use successive applications of the test to `back-out" the form of the time-varying intercept. We illustrate the methodology using an extended example concerning the demand for money
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Modelling Structural Change in Money Demand Using a Fourier-Series Approximation
2025Co-Authors: Ralf Becker, Walter Enders, Stan HurnAbstract:The paper develops a simple method that can be used to test for a time-varying intercept and to approximate its form. The test is solidly grounded in asymptotic theory and has good small-sample properties. The methodology is based on the fact that a Fourier approximation can capture the variation in any Absolutely Integrable Function of time. As such, it is possible to use successive applications of the test to "back-out" the form of the time-varying intercept. We illustrate the methodology using an extended example concerning the demand for money.structural break; fourier approximations; money demand
I K Purnaras - One of the best experts on this subject based on the ideXlab platform.
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complementary equations a fractional differential equation and a volterra integral equation
Electronic Journal of Qualitative Theory of Differential Equations, 2015Co-Authors: Leigh C Becker, T A Burton, I K PurnarasAbstract:It is shown that a continuous, Absolutely Integrable Function satisfies the initial value problem D q x(t) = f(t, x(t)), lim t!0+ t 1 q x(t) = x 0 (0 < q < 1)
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Complementary equations: a fractional differential equation and a Volterra integral equation
University of Szeged, 2015Co-Authors: Leigh Becker, Theodore Burton, I K PurnarasAbstract:It is shown that a continuous, Absolutely Integrable Function satisfies the initial value problem \[ D^{q}x(t) = f(t,x(t)), \qquad \lim_{t \to 0^+} t^{1-q}x(t) = x^{0} \qquad (0 < q < 1) \] on an interval $(0, T]$ if and only if it satisfies the Volterra integral equation \[ x(t) = x^{0}t^{q-1}+\frac{1}{\Gamma (q)}\int_{0}^{t}(t-s)^{q-1}f(s, x(s))\,ds \] on this same interval. In contradistinction to established existence theorems for these equations, no Lipschitz condition is imposed on $f(t,x)$. Examples with closed-form solutions illustrate this result