We study the action of metaplectic operators on Wiener amalgam spaces, giving upper bounds for their norms. As an application, we obtain new fixed-time estimates in these spaces for Schrodinger equations with general ...
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We study the action of metaplectic operators on Wiener amalgam spaces, giving upper bounds for their norms. As an application, we obtain new fixed-time estimates in these spaces for Schrodinger equations with general quadratic Hamiltonians and Strichartz estimates for the Schrodinger equation with potentials V(x) = +/-vertical bar x vertical bar(2). (C) 2007 Elsevier Inc. All rights reserved.
So-called short-time Fourier transform multipliers (also called Anti-Wick operators in the literature) arise by applying a pointwise multiplication operator to the STFT before applying the inverse STFT. Boundedness re...
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So-called short-time Fourier transform multipliers (also called Anti-Wick operators in the literature) arise by applying a pointwise multiplication operator to the STFT before applying the inverse STFT. Boundedness results are investigated for such operators on modulation spaces and on L-p-spaces. Because the proofs apply naturally to Wiener amalgam spaces the results are formulated in this context. Furthermore, a version of the Hardy-Littlewood inequality for the STFT is derived.
We construct a one-parameter family of algebras FIO(Xi, s), 0 <= s <= infinity, consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of the oper...
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We construct a one-parameter family of algebras FIO(Xi, s), 0 <= s <= infinity, consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of the operators in FIO(Xi, s). The operator algebra is defined by the decay properties of an associated Gabor matrix around the graph of the canonical transformation. In particular, for the limit case s = infinity, our Gabor technique provides a new approach to the analysis of S-0,0(0)-type Fourier integral operators, for which the global calculus represents a still open relevant problem. (C) 2012 Elsevier Masson SAS. All rights reserved.
We show that well-established methods from the theory of Banach modules and time-frequency analysis allow to derive completeness results for the collection of shifted and dilated version of a given (test) function in ...
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We show that well-established methods from the theory of Banach modules and time-frequency analysis allow to derive completeness results for the collection of shifted and dilated version of a given (test) function in a quite general setting. While the basic ideas show strong similarity to the arguments used in a recent paper by V. Katsnelson we extend his results in several directions, both relaxing the assumptions and widening the range of applications. There is no need for the Banach spaces considered to be embedded into (L2(R), 11 center dot 112), nor is the Hilbert space structure relevant. We choose to present the results in the setting of the Euclidean spaces, because then the Schwartz space S'(Rd) (d > 1) of tempered distributions provides a well-established environment for mathematical analysis. We also establish connections to modulation spaces and Shubin classes (Qs(Rd), 11 center dot 11Qs), showing that they are special cases of Katsnelson's setting (only) for s > 0.
We consider Banach algebras of infinite matrices defined in terms of a weight measuring the off-diagonal decay of the matrix entries. If a given matrix is invertible as an operator on we analyze the decay of its inver...
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We consider Banach algebras of infinite matrices defined in terms of a weight measuring the off-diagonal decay of the matrix entries. If a given matrix is invertible as an operator on we analyze the decay of its inverse matrix entries in the case where the matrix algebra is not inverse closed in the Banach algebra of bounded operators on To this end we consider a condition on sequences of weights which extends the notion of GRS-condition. Finally we focus on the behavior of inverses of pseudodifferential operators whose Weyl symbols belong to weighted modulation spaces and the weights lack the GRS condition.
In this article, spatial analyticity of solutions to Keller-Segel equation of parabolic-elliptic type with generalized dissipation is presented. First, we prove the analyticity of local solutions to system with large ...
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In this article, spatial analyticity of solutions to Keller-Segel equation of parabolic-elliptic type with generalized dissipation is presented. First, we prove the analyticity of local solutions to system with large rough initial data in modulation spaces with . Secondly, we establish the analyticity of solutions to the system with initial data in critical Fourier-Besov spaces with (or ) and , the main method is so-called Gevrey estimates, which is motivated by the works of Foias and Temam (Foias in Contemp Math 208:151-180, 1997). In the critical case that , we prove global Gevrey analyticity for small initial data in critical Fourier-Besov spaces with and . The results of us particularly imply temporal decay rates of higher Fourier-Besov norms of solutions.
We consider a class of Fourier integral operators, globally defined on R-d , with symbols and phases satisfying product type estimates (the so-called SG or scattering classes). We prove a sharp continuity result for s...
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We consider a class of Fourier integral operators, globally defined on R-d , with symbols and phases satisfying product type estimates (the so-called SG or scattering classes). We prove a sharp continuity result for such operators when acting on the modulation spaces M (p) . The minimal loss of derivatives is shown to be d broken vertical bar 1/2 - 1/p broken vertical bar. This global perspective produces a loss of decay as well, given by the same order. Strictly related, striking examples of unboundedness on L-p spaces are presented.
We study the action of Fourier Integral Operators (FIOs) of Hormander's type on FLp (R-d)(comp), 1 = 1, even for phases which are linear in the dual variables The proofs make use of tools from time-frequency analy...
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We study the action of Fourier Integral Operators (FIOs) of Hormander's type on FLp (R-d)(comp), 1 <= p <= infinity We see, from the Beurling-Helson theorem, that generally FIOs of order zero fail to be bounded oil these spaces when p not equal 2, the counterexample being given by any smooth non-linear change of variable Here we show that FIOs of order m = -d vertical bar 1/2 - 1/p vertical bar are instead bounded. Moreover, this loss of derivatives is proved to be sharp ill every dimension d >= 1, even for phases which are linear in the dual variables The proofs make use of tools from time-frequency analysis such as the theory of modulation spaces
In this paper, we study the Cauchy problem for Hartree type equation iu(t) + u(xx) = [K * vertical bar u vertical bar(2)] with Cauchy data in modulation spaces Mp,q(R). We establish global well-posedness results in Mp...
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In this paper, we study the Cauchy problem for Hartree type equation iu(t) + u(xx) = [K * vertical bar u vertical bar(2)] with Cauchy data in modulation spaces Mp,q(R). We establish global well-posedness results in Mp,p' (R) when K(x) = lambda/vertical bar x vertical bar(gamma), (lambda is an element of R, 0 < gamma < 1) with no smallness condition on initial data, where p' is the Holder conjugate of p. Our proof uses a splitting method inspired by the work of Vargas-Vega, Hyakuna-Tsutsumi, Grunrock and Chaichenets et al. to the modulation space setting and exploits polynomial growth of the Schrodinger propagator on modulation spaces. (c) 2022 Elsevier Inc. All rights reserved.
We obtain a class of subsets of R-2d such that the support of the short time Fourier transform (STFT) of a signal f is an element of L-2 (R-d) with respect to a window g is an element of L-2(R-d) cannot belong to this...
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We obtain a class of subsets of R-2d such that the support of the short time Fourier transform (STFT) of a signal f is an element of L-2 (R-d) with respect to a window g is an element of L-2(R-d) cannot belong to this class unless f or g is identically zero. Moreover we prove that the L-2-norm of the STFT is essentially concentrated in the complement of such a set. A generalization to other Hilbert spaces of functions or distributions is also provided. To this aim we obtain some results on compactness of localization operators acting on weighted modulation Hilbert spaces. (C) 2010 Elsevier Inc. All rights reserved.
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