| 1 |
,Strongly Elliptic Second Order Systems with Spectral Parameter in Transmission Conditions on a Nonclosed Surface, |
M.S. Agranovich |
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Abstract
We consider a class of second order strongly elliptic systems in ℝ., . ≥ 3, outside a bounded nonclosed surface . with transmission conditions on . containing a spectral parameter. Assuming that . and its boundary γ are Lipschitz, we reduce the problems to spectral equations on . for operators of potential type. We prove the invertibility of these operators in suitable Sobolev type spaces and indicate spectral consequences. Simultaneously, we prove the unique solvability of the Dirichlet and Neumann problems with boundary data on ..
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| 2 |
,Strongly Elliptic Second Order Systems with Spectral Parameter in Transmission Conditions on a Nonclosed Surface, |
M.S. Agranovich |
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Abstract
We consider a class of second order strongly elliptic systems in ℝ., . ≥ 3, outside a bounded nonclosed surface . with transmission conditions on . containing a spectral parameter. Assuming that . and its boundary γ are Lipschitz, we reduce the problems to spectral equations on . for operators of potential type. We prove the invertibility of these operators in suitable Sobolev type spaces and indicate spectral consequences. Simultaneously, we prove the unique solvability of the Dirichlet and Neumann problems with boundary data on ..
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| 3 |
,Well-Posedness of the Cauchy Problem for Some Degenerate Hyperbolic Operators, |
Alessia Ascanelli,Massimo Cicognani |
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Abstract
We use an uniform approach to different kinds of degenerate hyperbolic Cauchy problems to prove well-posedness in . and in Gevrey classes. We prove in particular that we can treat by the same method a weakly hyperbolic problem, satisfying an intermediate condition between effective hyperbolicity and the Levi condition, and a strictly hyperbolic problem with non-regular coefficients with respect to the time variable.
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| 4 |
,Well-Posedness of the Cauchy Problem for Some Degenerate Hyperbolic Operators, |
Alessia Ascanelli,Massimo Cicognani |
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Abstract
We use an uniform approach to different kinds of degenerate hyperbolic Cauchy problems to prove well-posedness in . and in Gevrey classes. We prove in particular that we can treat by the same method a weakly hyperbolic problem, satisfying an intermediate condition between effective hyperbolicity and the Levi condition, and a strictly hyperbolic problem with non-regular coefficients with respect to the time variable.
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| 5 |
,Quasilinear Hyperbolic Equations with SG-Coefficients, |
Marco Cappiello,Luisa Zanghirati |
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Abstract
We study some classes of quasilinear symmetric hyperbolic systems with coefficients of SG type. We obtain results of existence and uniqueness for the solution in some weighted Sobolev spaces.
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| 6 |
,Quasilinear Hyperbolic Equations with SG-Coefficients, |
Marco Cappiello,Luisa Zanghirati |
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Abstract
We study some classes of quasilinear symmetric hyperbolic systems with coefficients of SG type. We obtain results of existence and uniqueness for the solution in some weighted Sobolev spaces.
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| 7 |
,Representation of Solutions and Regularity Properties for Weakly Hyperbolic Systems, |
Ilia Kamotski,Michael Ruzhansky |
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Abstract
Regularity properties of generic hyperbolic systems with diagonalizable principal part will be established in . and other function spaces. Sharp regularity of solutions will be discussed. Applications will be given to solutions of scalar weakly hyperbolic equations with non-involutive characteristics. Established representation of solutions and its properties allow to derive spectral asymptotics for elliptic systems with diagonalizable principal part.
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| 8 |
,Representation of Solutions and Regularity Properties for Weakly Hyperbolic Systems, |
Ilia Kamotski,Michael Ruzhansky |
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Abstract
Regularity properties of generic hyperbolic systems with diagonalizable principal part will be established in . and other function spaces. Sharp regularity of solutions will be discussed. Applications will be given to solutions of scalar weakly hyperbolic equations with non-involutive characteristics. Established representation of solutions and its properties allow to derive spectral asymptotics for elliptic systems with diagonalizable principal part.
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| 9 |
,Global Calculus of Fourier Integral Operators, Weighted Estimates, and Applications to Global Analysis of Hyperbolic Equations, |
Michael Ruzhansky,Mitsuru Sugimoto |
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Abstract
The aim of this paper is to present certain global regularity properties of hyperbolic equations. In particular, it will be determined in what way the global decay of Cauchy data implies the global decay of solutions. For this purpose, global weighted estimates in Sobolev spaces for Fourier integral operators will be reviewed. We will also present elements of the global calculus under minimal decay assumptions on phases and amplitudes.
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| 10 |
,Global Calculus of Fourier Integral Operators, Weighted Estimates, and Applications to Global Analysis of Hyperbolic Equations, |
Michael Ruzhansky,Mitsuru Sugimoto |
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Abstract
The aim of this paper is to present certain global regularity properties of hyperbolic equations. In particular, it will be determined in what way the global decay of Cauchy data implies the global decay of solutions. For this purpose, global weighted estimates in Sobolev spaces for Fourier integral operators will be reviewed. We will also present elements of the global calculus under minimal decay assumptions on phases and amplitudes.
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| 11 |
,-Continuity for Pseudo-Differential Operators, |
Gianluca Garello,Alessandro Morando |
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Abstract
The authors give a short survey about the .-continuity of pseudodifferential operators both with smooth and non-smooth symbols
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| 12 |
,-Continuity for Pseudo-Differential Operators, |
Gianluca Garello,Alessandro Morando |
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Abstract
The authors give a short survey about the .-continuity of pseudodifferential operators both with smooth and non-smooth symbols
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| 13 |
,Fredholm Property of Pseudo-Differential Operators on Weighted Hölder-Zygmund Spaces, |
V.S. Rabinovich |
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Abstract
We consider pseudo-differential operators in the L.Hörmander class . acting on Hölder-Zygmund spaces with exponential weights. The necessary and sufficient conditions for operators under consideration to be Fredholm and a description of their essential spectra have been obtained. We also prove the Fragmen-Lindelöf principle for exponential decreasing of solutions of pseudo-differential equations.
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| 14 |
,Fredholm Property of Pseudo-Differential Operators on Weighted Hölder-Zygmund Spaces, |
V.S. Rabinovich |
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Abstract
We consider pseudo-differential operators in the L.Hörmander class . acting on Hölder-Zygmund spaces with exponential weights. The necessary and sufficient conditions for operators under consideration to be Fredholm and a description of their essential spectra have been obtained. We also prove the Fragmen-Lindelöf principle for exponential decreasing of solutions of pseudo-differential equations.
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| 15 |
,Weyl Transforms and Convolution Operators on the Heisenberg Group, |
M.W. Wong |
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Abstract
The Fourier transform on the Heisenberg group, the Fourier transform along the center of the Heisenberg group and the Euclidean Fourier transform are used to prove that Weyl transforms and convolution operators on the Heisenberg group are, respectively, classical Weyl transforms and pseudo-differential operators.
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| 16 |
,Weyl Transforms and Convolution Operators on the Heisenberg Group, |
M.W. Wong |
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Abstract
The Fourier transform on the Heisenberg group, the Fourier transform along the center of the Heisenberg group and the Euclidean Fourier transform are used to prove that Weyl transforms and convolution operators on the Heisenberg group are, respectively, classical Weyl transforms and pseudo-differential operators.
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| 17 |
,Uncertainty Principle, Phase Space Ellipsoids and Weyl Calculus, |
Maurice de Gosson |
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Abstract
We state a precise form of the uncertainty principle in terms of phase space ellipsoids, which we then express in terms of the symplectic capacity of phase space ellipsoids. We apply our approach to the study of the positivity of the Wigner transform of a pure quantum state, and of that of the Weyl operator associated to the average of a positive symbol over a phase space ellipsoid.
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| 18 |
,Uncertainty Principle, Phase Space Ellipsoids and Weyl Calculus, |
Maurice de Gosson |
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Abstract
We state a precise form of the uncertainty principle in terms of phase space ellipsoids, which we then express in terms of the symplectic capacity of phase space ellipsoids. We apply our approach to the study of the positivity of the Wigner transform of a pure quantum state, and of that of the Weyl operator associated to the average of a positive symbol over a phase space ellipsoid.
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| 19 |
,Pseudo-Differential Operator and Reproducing Kernels Arising in Geometric Quantization, |
Kenro Furutani |
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Abstract
We show that an operator defined on the quaternion projective space is a zeroth order selfadjoint pseudo-differential operator of Hörmander class .. This operator arises when we compare two quantization operators of the geodesic flow on the quaternion projective space. Such quantization operators are defined on a Hilbert space consisting of holomorphic functions and the Hilbert space has reproducing kernel. We describe the reproducing kernels in the cases of sphere and quaternion projective space in terms of hypergeometric functions, and discuss their relation through fiber integration with respect to the complexified Hopf fibration.
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| 20 |
,Pseudo-Differential Operator and Reproducing Kernels Arising in Geometric Quantization, |
Kenro Furutani |
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Abstract
We show that an operator defined on the quaternion projective space is a zeroth order selfadjoint pseudo-differential operator of Hörmander class .. This operator arises when we compare two quantization operators of the geodesic flow on the quaternion projective space. Such quantization operators are defined on a Hilbert space consisting of holomorphic functions and the Hilbert space has reproducing kernel. We describe the reproducing kernels in the cases of sphere and quaternion projective space in terms of hypergeometric functions, and discuss their relation through fiber integration with respect to the complexified Hopf fibration.
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| 21 |
,Hudson’s Theorem and Rank One Operators in Weyl Calculus, |
Joachim Toft |
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Abstract
A proof of Hudson’s theorem in several dimension is presented. Some consequences for pseudo-differential operators of rank one are given.
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| 22 |
,Hudson’s Theorem and Rank One Operators in Weyl Calculus, |
Joachim Toft |
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Abstract
A proof of Hudson’s theorem in several dimension is presented. Some consequences for pseudo-differential operators of rank one are given.
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| 23 |
,Distributions and Pseudo-Differential Operators on Infinite-Dimensional Spaces with Applications in Quantum Physics, |
Andrei Khrennikov |
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Abstract
This paper is the review on theory of infinite-dimensional pseudo-differential operators(PDO) and their application to quantization of systems with the infinite number of degrees of freedom. There are considered various approaches to the theory of infinite-dimensional PDO (e.g., Berezin’s approach based on polynomial operators). There is presented in details the calculus of PDO based on the theory of distributions on infinite-dimensional spaces (general locally convex spaces). This calculus is based on the “Feynman measure” on the phase space (introduced by Smolyanov in 80th). Symbols of the most important PDO in the representation of second quantization are calculated.
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| 24 |
,Distributions and Pseudo-Differential Operators on Infinite-Dimensional Spaces with Applications in Quantum Physics, |
Andrei Khrennikov |
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Abstract
This paper is the review on theory of infinite-dimensional pseudo-differential operators(PDO) and their application to quantization of systems with the infinite number of degrees of freedom. There are considered various approaches to the theory of infinite-dimensional PDO (e.g., Berezin’s approach based on polynomial operators). There is presented in details the calculus of PDO based on the theory of distributions on infinite-dimensional spaces (general locally convex spaces). This calculus is based on the “Feynman measure” on the phase space (introduced by Smolyanov in 80th). Symbols of the most important PDO in the representation of second quantization are calculated.
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| 25 |
,Ultradistributions and Time-Frequency Analysis, |
Nenad Teofanov |
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Abstract
The aim of the paper is to show the connection between the theory of ultradistributions and time-frequency analysis. This is done through time-frequency representations and modulation spaces. Furthermore, some classes of pseudo-differential operators are observed.
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| 26 |
,Ultradistributions and Time-Frequency Analysis, |
Nenad Teofanov |
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Abstract
The aim of the paper is to show the connection between the theory of ultradistributions and time-frequency analysis. This is done through time-frequency representations and modulation spaces. Furthermore, some classes of pseudo-differential operators are observed.
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| 27 |
,Frames and Generalized Shift-Invariant Systems, |
Ole Christensen |
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Abstract
With motivation from the theory of Hilbert-Schmidt operators we review recent topics concerning frames in .(ℝ) and their duals. Frames are generalizations of orthonormal bases in Hilbert spaces. As for an orthonormal basis, a frame allows each element in the underlying Hilbert space to be written as an unconditionally convergent infinite linear combination of the frame elements; however, in contrast to the situation for a basis, the coefficients might not be unique. We present the basic facts from frame theory and the motivation for the fact that most recent research concentrates on tight frames or dual frame pairs rather than general frames and their canonical dual. The corresponding results for Gabor frames and wavelet frames are discussed in detail.
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| 28 |
,Frames and Generalized Shift-Invariant Systems, |
Ole Christensen |
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Abstract
With motivation from the theory of Hilbert-Schmidt operators we review recent topics concerning frames in .(ℝ) and their duals. Frames are generalizations of orthonormal bases in Hilbert spaces. As for an orthonormal basis, a frame allows each element in the underlying Hilbert space to be written as an unconditionally convergent infinite linear combination of the frame elements; however, in contrast to the situation for a basis, the coefficients might not be unique. We present the basic facts from frame theory and the motivation for the fact that most recent research concentrates on tight frames or dual frame pairs rather than general frames and their canonical dual. The corresponding results for Gabor frames and wavelet frames are discussed in detail.
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| 29 |
,The Wigner Distribution of Gaussian Weakly Harmonizable Stochastic Processes, |
Patrik Wahlberg |
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Abstract
The paper treats the Wigner distribution of scalar-valued stochastic processes defined on ℝ.. We show that if the process is Gaussian and weakly harmonizable then a stochastic Wigner distribution is well defined. The special case of stationary processes is studied, in which case the Wigner distribution is weakly stationary in the time variable and the variance is equal to the deterministic Wigner distribution of the covariance function.
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| 30 |
,The Wigner Distribution of Gaussian Weakly Harmonizable Stochastic Processes, |
Patrik Wahlberg |
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Abstract
The paper treats the Wigner distribution of scalar-valued stochastic processes defined on ℝ.. We show that if the process is Gaussian and weakly harmonizable then a stochastic Wigner distribution is well defined. The special case of stationary processes is studied, in which case the Wigner distribution is weakly stationary in the time variable and the variance is equal to the deterministic Wigner distribution of the covariance function.
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| 31 |
,Reproducing Groups for the Metaplectic Representation, |
E. Cordero,F. De Mari,K. Nowak,A. Tabacco |
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Abstract
We consider the (extended) metaplectic representation of the semidirect product . of the symplectic group and the Heisenberg group. By looking at the standard resolution of the identity formula and inspired by previous work [5], [13], [4], we introduce the notion of admissible (reproducing) subgroup of . via the Wigner distribution. We prove some features of admissible groups and then exhibit an explicit example (. = 2) of such a group, in connection with wavelet theory.
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| 32 |
,Reproducing Groups for the Metaplectic Representation, |
E. Cordero,F. De Mari,K. Nowak,A. Tabacco |
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Abstract
We consider the (extended) metaplectic representation of the semidirect product . of the symplectic group and the Heisenberg group. By looking at the standard resolution of the identity formula and inspired by previous work [5], [13], [4], we introduce the notion of admissible (reproducing) subgroup of . via the Wigner distribution. We prove some features of admissible groups and then exhibit an explicit example (. = 2) of such a group, in connection with wavelet theory.
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发表于 2025-3-21 17:19:46
