The Segal algebra \(\mathbf S_0(\mathbb R^d)\) and norm summability of Fourier series and Fourier transforms

DOI10.1007/s00605-005-0358-4zbMath1130.42012OpenAlexW2067796307MaRDI QIDQ2503139

Ferenc Weisz, Hans G. Feichtinger

Publication date: 14 September 2006

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-005-0358-4

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) (H^p)-spaces (42B30) Summability in several variables (42B08)

Related Items (36)

On a (no longer) new Segal algebra: a review of the Feichtinger algebra ⋮ Lebesgue points and restricted convergence of Fourier transforms and Fourier series ⋮ Inverse continuous wavelet transform in pringsheim's sense on Wiener amalgam spaces ⋮ On Fourier integral operators with Hölder-continuous phase ⋮ Multi-dimensional Fourier transforms, Lebesgue points and strong summability ⋮ Quasi-interpolation in the Fourier algebra ⋮ Inverse continuous wavelet transform in weighted variable exponent amalgam spaces ⋮ Restricted summability of Fourier transforms and local Hardy spaces ⋮ Higher Dimensional Continuous Wavelet Transform in Wiener Amalgam Spaces ⋮ Strong summability of Fourier transforms at Lebesgue points and Wiener amalgam spaces ⋮ Pointwise convergence in Pringsheim's sense of the summability of Fourier transforms on Wiener amalgam spaces ⋮ Lebesgue points of two-dimensional Fourier transforms and strong summability ⋮ Monotonicity of certain left and right Riemann sums ⋮ Herz spaces and restricted summability of Fourier transforms and Fourier series ⋮ \(\ell _{1}\)-summability of higher-dimensional Fourier series ⋮ Inversion formulas for the short-time Fourier transform ⋮ Inversion formulas for the continuous wavelet transform ⋮ Restricted convergence of the inverse continuous wavelet transform ⋮ Wiener amalgams, Hardy spaces and summability of Fourier series ⋮ Globally well and ill posedness for non-elliptic derivative Schrödinger equations with small rough data ⋮ Summability of Fourier series in periodic Hardy spaces with variable exponent ⋮ Universal series induced by approximate identities and some relevant applications ⋮ \(\ell_{1}\)-summability of \(d\)-dimensional Fourier transforms ⋮ On approximation methods generated by Bochner-Riesz kernels ⋮ Lebesgue points of double Fourier series and strong summability ⋮ Marcinkiewicz summability of Fourier series, Lebesgue points and strong summability ⋮ Convergence of multi-dimensional integral operators and applications ⋮ Summability of Gabor expansions and Hardy spaces ⋮ \(\ell_1\)-summability and Lebesgue points of \(d\)-dimensional Fourier transforms ⋮ Iterative deconvolution for kernels with strictly positive Fourier transforms ⋮ Local well-posedness for the Davey-Stewartson equation in a generalized Feichtinger algebra ⋮ Pointwise summability of Gabor expansions ⋮ Local Hardy spaces and summability of Fourier transforms ⋮ Cesàro summability and Lebesgue points of higher dimensional Fourier series ⋮ Besov spaces with generalized smoothness and summability of multiple Fourier series ⋮ Summability of Fourier transforms on mixed-norm Lebesgue spaces via associated Herz spaces

Cites Work

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• \(L^\infty\) system approximation algorithms generated by \(\varphi\) summations
• On a new Segal algebra
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• Topics in approximation theory
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• l-1 summability of multiple Fourier integrals and positivity
• Embeddings of some classical Banach spaces into modulation spaces
• Operator–valued Fourier multiplier theorems on Besov spaces
• Wiener amalgams and pointwise summability of Fourier transforms and Fourier series
• On \(\ell-1\) Riesz summability of the inverse Fourier integral
• On the summability of trigonometric interpolation processes
• On uniform convergence of sequences of certain linear operators

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