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Article
Dilation estimates for Wiener amalgam spaces of Orlicz type
We extend dilation properties of Wiener amalgam spaces when the local and global componenets are Lebesgue spaces to a more general setting of Orlicz spaces. We recover the result of Cordero and Nicola when res...
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Chapter
An Excursion to Multiplications and Convolutions on Modulation Spaces
We give a self-contained introduction to (quasi-)Banach modulation spaces of ultradistributions, and review results on boundedness for multiplications and convolutions for elements in such spaces. Furthermore,...
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Article
Open AccessSubexponential decay and regularity estimates for eigenfunctions of localization operators
We consider time-frequency localization operators \(A_a^{\varphi _1,\varphi _2}\) A ...
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Article
Bilinear Pseudo-differential Operators with Gevrey–Hörmander Symbols
We consider bilinear pseudo-differential operators whose symbols may have a sub-exponential growth at infinity, together with all their derivatives. It is proved that those symbol classes can be described by t...
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Article
A Paley–Wiener theorem in extended Gevrey regularity
In this paper we introduce appropriate associated function to the sequence \(M_p=p^{\tau p^{\sigma }}, p\in {\mathbf {N}}, \tau>0, \sigma >1\)Mp=pτpσ,p∈N,τ>0,σ>1, and derive its sharp asymptotic estimates in term...
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Article
Multiresolution expansions and wavelets in Gelfand–Shilov spaces
We study approximation properties generated by highly regular scaling functions and orthonormal wavelets. These properties are conveniently described in the framework of Gelfand–Shilov spaces. Important exampl...
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Chapter
Extended Gevrey Regularity via the Short-Time Fourier Transform
We study the regularity of smooth functions whose derivatives are dominated by sequences of the form M p τ , σ = p τ p σ \(M_p^{\tau ,\sigma }=p^{\tau p^{\sigma }}\) , τ > 0, σ ≥ 1. We ...
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Chapter
The Shearlet Transform and Lizorkin Spaces
We prove a continuity result for the shearlet transform when restricted to the space of smooth and rapidly decreasing functions with all vanishing moments. We define the dual shearlet transform, called here th...
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Chapter
Continuity Properties of Multilinear Localization Operators on Modulation Spaces
We introduce multilinear localization operators in terms of the short-time Fourier transform and multilinear Weyl pseudodifferential operators. We prove that such localization operators are in fact Weyl pseudo...
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Chapter and Conference Paper
The Grossmann–Royer Transform, Gelfand–Shilov Spaces, and Continuity Properties of Localization Operators on Modulation Spaces
This paper offers a review of results concerning localization operators on modulation spaces, and related topics. However, our approach, based on the Grossmann–Royer transform, gives a new insight and (slightl...
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Article
Inverse closedness and localization in extended Gevrey regularity
We consider classes \( \mathcal {E}_{\tau ,\sigma }(U)\) ...
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Chapter
Ultradifferentiable Functions of Class \( M_p^{\tau ,\sigma } \) and Microlocal Regularity
We study spaces of ultradifferentiable functions which contain Gevrey classes. Although the corresponding defining sequences do not satisfy Komatsu’s condition (M.2)’, we prove appropriate continuity propertie...
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Article
The wavelet transforms in Gelfand–Shilov spaces
We describe local and global behavior of wavelet transforms of ultra-differentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand–Shilov type spaces ...
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Article
Continuity and Schatten–von Neumann Properties for Localization Operators on Modulation Spaces
We use sharp convolution estimates for weighted Lebesgue and modulation spaces to obtain an extension of the celebrated Cordero-Gröchenig theorems on boundedness and Schatten–von Neumann properties of localiza...
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Article
Beyond Gevrey regularity
We define and study classes of smooth functions which are less regular than Gevrey functions. To that end we introduce two-parameter dependent sequences which do not satisfy Komatsu’s condition (M.2)’, which i...
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Chapter and Conference Paper
A Note on Wave-front Sets of Roumieu Type Ultradistributions
We study wave-front sets in weighted Fourier–Lebesgue spaces and corresponding spaces of ultradistributions. We give a comparison of these sets with the well-known wave-front sets of Roumieu type ultradistribu...
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Article
Gabor pairs, and a discrete approach to wave-front sets
We introduce admissible lattices and Gabor pairs to define discrete versions of wave-front sets with respect to Fourier–Lebesgue and modulation spaces. We prove that these wave-front sets agree with each other...
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Chapter and Conference Paper
Relating the Astronomical Timescale to the Loess–Paleosol Sequences in Vojvodina, Northern Serbia
In this study the first astronomical time scale for loess-paleosol sequences of Vojvodina region, northern Serbia is presented astronomical timescale for the loess–paleosol sequences of the Vojvodina region, n...
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Article
Micro-Local Analysis with Fourier Lebesgue Spaces. Part I
Let ω,ω 0 be appropriate weight functions and q∈[1,∞]. We introduce the wave-front set, $\mathrm{WF}_{\mathcal...
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Chapter
Singular Support and \(\mathfrak{F}\) L q Continuity of Pseudodifferential Operators
In this paper we show possible directions for numerical mathematicians interested in the approximation of different types of singular supports, wave front sets and of pseudodifferential operators in the framew...
