We consider the Cauchy problem of the modified Dispersion-Generalized Benjamin Ono equations on the real line. We prove some optimal local well-posedness results in the modulation spaces. The main new ingredient is an...
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We consider the Cauchy problem of the modified Dispersion-Generalized Benjamin Ono equations on the real line. We prove some optimal local well-posedness results in the modulation spaces. The main new ingredient is an improved version of bilinear Strichartz estimates in modulation space. (c) 2021 Elsevier Inc. All rights reserved.
In this paper, we consider the trace theorem for modulation spaces M-p,q(s), alpha-modulation spaces M-p,q(s,alpha) and Besov spaces B-p,q(s). For the modulation space, we obtain the sharp results. (C) 2010 Elsevier I...
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In this paper, we consider the trace theorem for modulation spaces M-p,q(s), alpha-modulation spaces M-p,q(s,alpha) and Besov spaces B-p,q(s). For the modulation space, we obtain the sharp results. (C) 2010 Elsevier Inc. All rights reserved.
Applying the frequency-uniform decomposition technique, we study the Cauchy problem for derivative Ginzburg-Landau equation u(t) = (nu + i)Delta u + del (vertical bar u vertical bar(2) u) + (lambda(2) . del u)vertical...
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Applying the frequency-uniform decomposition technique, we study the Cauchy problem for derivative Ginzburg-Landau equation u(t) = (nu + i)Delta u + del (vertical bar u vertical bar(2) u) + (lambda(2) . del u)vertical bar u vertical bar(2) + alpha vertical bar u vertical bar(2 delta)u, where delta is an element of N, lambda(1), lambda(2) are complex constant vectors, nu is an element of [0, 1], alpha is an element of C. For n >= 3, we show that it is uniformly global well posed for all v E [0,11 if initial data u0 in modulation space M-2,1(s) and Sobolev spaces Hs+n/2 (s > 3) and parallel to u(0)parallel to L-2 is small enough. Moreover. we show that its solution will converge to that of the derivative Schrodinger equation in C(0, T;L-2) if nu -> 0 and u(0) in M-2,1(s) or Hs+n/2 with s > 4. For n = 2, we obtain the local well-posedness results and inviscid limit with the Cauchy data in M-1,1(s) (s > 3) and parallel to u(0)parallel to L-1 <<1. (C) 2011 Elsevier Inc. All rights reserved.
We introduce modulation type spaces associated with the generators of polynomially bounded groups. Besides strongly continuous groups we study in detail the case of bi-continuous groups, e.g. weak-continuous groups in...
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We introduce modulation type spaces associated with the generators of polynomially bounded groups. Besides strongly continuous groups we study in detail the case of bi-continuous groups, e.g. weak-continuous groups in dual spaces. It turns out that this gives new insight in situations where generators are not densely defined. Classical modulation spaces are covered as a special case but the abstract formulation gives more flexibility. We illustrate this with an application to a nonlinear Schrodinger equation.
The purpose of this paper is to study the multipliers on modulation spaces M p,q(R d) for 0 K (K > d/(2p) and K ∈ N), consisting of all functions f ∈ C K whose derivatives ∂ α f ∈ L ∞ for any multi-index α su...
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The purpose of this paper is to study the multipliers on modulation spaces M p,q(R d) for 0 < p,q < ∞. In particular, it is shown in the case 0 < p < 1 that elements of B K (K > d/(2p) and K ∈ N), consisting of all functions f ∈ C K whose derivatives ∂ α f ∈ L ∞ for any multi-index α such that |α| ≦ K, are multipliers on M p,q.
For any appropriate weight function ω, spaces are introduced as counterimage of unweighted modulation spaces through Toeplitz operators with symbol ω. It is proved that the weighted modulation spaces coincide with t...
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Let H be a Hilbert space, continuously embedded in S'(R-d), and which contains at least one non-zero element in S'(R-d). If there is a constant C-0 > 0 such that ||e(i ,xi >)f ( -x)||(H) < C-0||f||(...
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Let H be a Hilbert space, continuously embedded in S'(R-d), and which contains at least one non-zero element in S'(R-d). If there is a constant C-0 > 0 such that ||e(i < ,xi >)f ( -x)||(H) < C-0||f||(H), f is an element of H, x, xi is an element of R-d, then we prove that H = L-2(R-d), with equivalent norms. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).
In this paper, we establish the validity of the so-called Bounded Approximation Property (BAP) for a comprehensive class of translation and modulation invariant Banach spaces (B, parallel to . parallel to(B)) of tempe...
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In this paper, we establish the validity of the so-called Bounded Approximation Property (BAP) for a comprehensive class of translation and modulation invariant Banach spaces (B, parallel to . parallel to(B)) of tempered distributions on the Euclidean space R-d. In fact, such spaces have a double module structure, over some Beurling algebra with respect to convolution, and with respect to pointwise multiplication over some Fourier Beurling algebra. Combining this double module structure with functional analytic arguments which describe the approximation of convolution operators by discrete convolutions we are able to verify the BAP, in fact, for most cases even the Metric Approximation Property (MAP) for such Banach space. The family of spaces under consideration is very rich and contains virtually all the classical function spaces relevant for mathematical analysis, as long as the Schwartz space S(R-d) is dense in (B, parallel to . parallel to(B)). In particular, all the reflexive spaces in this family are included. Moreover, this family of Banach spaces is closed with respect to intersections, sums and various interpolation methods.
In this paper various properties of global and local changes of variables as well as properties of canonical transforms are investigated on modulation and Wiener amalgam spaces. We establish several relations among lo...
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In this paper various properties of global and local changes of variables as well as properties of canonical transforms are investigated on modulation and Wiener amalgam spaces. We establish several relations among localisations of such spaces and, as a consequence, we obtain several versions of local and global Beurling-Helson type theorems. We also establish a number of positive results such as local boundedness of canonical transforms on modulation spaces, properties of homogeneous changes of variables, and local continuity of Fourier integral operators on F L-q. Finally, counterparts of these results are discussed for spaces on the torus. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Let H be a Hilbert space of distributions on R-d which contains at least one non-zero element of the Feichtinger algebra S-0 and is continuously embedded in D'. If H is translation and modulation invariant, also i...
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Let H be a Hilbert space of distributions on R-d which contains at least one non-zero element of the Feichtinger algebra S-0 and is continuously embedded in D'. If H is translation and modulation invariant, also in the sense of its norm, then we prove that H = L-2, with the same norm apart from a multiplicative constant.
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