We prove that pseudo-differential operators with symbols in the class S-1,delta(0) ( 0 < delta < 1) are not always bounded on the modulation space M-p,M-q ( q not equal 2).
We prove that pseudo-differential operators with symbols in the class S-1,delta(0) ( 0 < delta < 1) are not always bounded on the modulation space M-p,M-q ( q not equal 2).
We discuss when the nonlinear operation f -> F(f) maps the modulation space M-s(pg) (R-n) (1 n = n/q, hence it is true for this space if F is entire. We claim that it is still true for non-analytic F when q >= ...
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We discuss when the nonlinear operation f -> F(f) maps the modulation space M-s(pg) (R-n) (1 <= p,q <= oo) to the same space again. It is known that M-s(pg) (R-n) p= (R-n) is a multiplication algebra when s > n = n/q, hence it is true for this space if F is entire. We claim that it is still true for non-analytic F when q >= 4/3. (C) 2019 Elsevier Inc. All rights reserved.
We obtain Gabor frame characterizations of modulation spaces defined via a broad class of translation-modulation invariant Banach spaces of distributions. We show that these spaces admit an atomic decomposition throug...
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We obtain Gabor frame characterizations of modulation spaces defined via a broad class of translation-modulation invariant Banach spaces of distributions. We show that these spaces admit an atomic decomposition through Gabor expansions and that they are characterized by summability properties of their Gabor coefficients. Furthermore, we construct a large space of admissible windows. This generalizes and unifies several fundamental results for the classical modulation spaces Mwp,q and the amalgam spaces W(Lp,L wq). Due to the absence of solidity assumptions on the Banach spaces defining these generalized modulation spaces, the methods used for the spaces Mwp,q (or, more generally, in coorbit space theory) fail in our setting and we develop here a new approach based on the twisted convolution.
The aim of this paper is two fold. We show that if a complex function F   on CC operates in the modulation spaces Mp,1(Rn)Mp,1(Rn) by composition, then F   is real analytic on R2≈CR2&as...
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The aim of this paper is two fold. We show that if a complex function F on CC operates in the modulation spaces Mp,1(Rn)Mp,1(Rn) by composition, then F is real analytic on R2≈CR2≈C. This answers negatively, the open question posed in Ruzhansky et al. (2012) [21], regarding the general power type nonlinearity of the form |u|αu|u|αu. We also characterise the functions that operate in the modulation space M1,1(Rn)M1,1(Rn).The local well-posedness of the NLS, NLW and NLKG equations for the ‘real entire’ nonlinearities are also studied in some weighted modulation spaces Msp,q(Rn).
We study the Cauchy problem for an incompressible magneto-hydrodynamics (MHD) system in the modulation space M-q,sigma(s) (R-n) (n >= 2) with initial data (u(0), b(0)) is an element of PMq,sigma s (R-n) x PMq,sigma...
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We study the Cauchy problem for an incompressible magneto-hydrodynamics (MHD) system in the modulation space M-q,sigma(s) (R-n) (n >= 2) with initial data (u(0), b(0)) is an element of PMq,sigma s (R-n) x PMq,sigma s (R-n). We prove that this problem is locally well-posed in such a space when 1 <= q <= infinity, 1 <= sigma < infinity and n(sigma-1)/sigma - 1 <= s, and globally well-posed when 1 <= q <= n, n/n-1 <= sigma < infinity and max{n(sigma-1)/sigma -1, n(sigma-2)/sigma} < s < n(sigma-1)/sigma. (C) 2011 Elsevier Inc. All rights reserved.
We deduce trace properties for modulation spaces (including certain Wiener-amalgam spaces) of Gelfand-Shilov *** use these results to show that psi dos with amplitudes in suitable modulation spaces, agree with normal ...
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We deduce trace properties for modulation spaces (including certain Wiener-amalgam spaces) of Gelfand-Shilov *** use these results to show that psi dos with amplitudes in suitable modulation spaces, agree with normal type psi dos whose symbols belong to (other) modulation spaces. In particular we extend earlier trace results for modulation spaces, to include quasi-Banach modulation spaces. We also apply our results to extend earlier results on Schatten-von Neumann and nuclear properties for psi dos with amplitudes in modulation spaces.
We give sufficient and necessary conditions on the Lebesgue exponents for the Weyl product to be bounded on modulation spaces. The sufficient conditions are obtained as the restriction to N = 2 of a result valid for t...
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We give sufficient and necessary conditions on the Lebesgue exponents for the Weyl product to be bounded on modulation spaces. The sufficient conditions are obtained as the restriction to N = 2 of a result valid for the N-fold Weyl product. As a byproduct, we obtain sharp conditions for the twisted convolution to be bounded on Wiener amalgam spaces. (C) 2014 Elsevier Inc. All rights reserved.
In this paper we study the Cauchy problem for the generalized Boussinesq equation with initial data in modulation spaces M-p',q(s) (R-n), n >= 1. After a decomposition of the Boussinesq equation in a 2 x 2-nonl...
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In this paper we study the Cauchy problem for the generalized Boussinesq equation with initial data in modulation spaces M-p',q(s) (R-n), n >= 1. After a decomposition of the Boussinesq equation in a 2 x 2-nonlinear system, we obtain the existence of global and local solutions in several classes of functions with values in M-p,q(s) x D(-1)JM(p,q)(s) spaces for suitable p, q and s, including the special case p = 2, q = 1 and s = 0. Finally, we prove some results of scattering and asymptotic stability in the framework of modulation spaces.
We discuss algebraic properties of the Weyl product acting on modulation spaces. For a certain class of weight functions omega we prove that M((omega))(p,q) is an algebra under the Weyl product if p epsilon [1, infini...
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We discuss algebraic properties of the Weyl product acting on modulation spaces. For a certain class of weight functions omega we prove that M((omega))(p,q) is an algebra under the Weyl product if p epsilon [1, infinity] and 1 <= q <= min(p, p '). For the remaining cases P epsilon [1, infinity] and min(p, p ') < q <= infinity we show that the unweighted spaces M(p,q) are not algebras under the Weyl product. (C) 2007 Elsevier Inc. All rights reserved.
We study continuity properties on modulation spaces for tau-pseudodifferential operators Op(tau) (a) with symbols a in Wiener amalgam spaces. We obtain boundedness results for tau is an element of(0, 1) whereas, in th...
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We study continuity properties on modulation spaces for tau-pseudodifferential operators Op(tau) (a) with symbols a in Wiener amalgam spaces. We obtain boundedness results for tau is an element of(0, 1) whereas, in the end-points tau = 0 and tau = 1, the corresponding operators are in general unbounded. Furthermore, for tau is an element of(0, 1), we exhibit a function of tau which is an upper bound for the operator norm. The continuity properties of Op(tau) (a), for any tau is an element of[0, 1], with symbols a in modulation spaces are well known. Here we find an upper bound for the operator norm which does not depend on the parameter tau is an element of[0, 1], as expected. Key ingredients are uniform continuity estimates for tau-Wigner distributions. (C) 2018 Elsevier Inc. All rights reserved.
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