Kernel Theorems for Modulation Spaces
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DOI: 10.1007/s00041-017-9573-3
Abstract: We deal with kernel theorems for modulation spaces. We completely characterize the continuity of a linear operator on the modulation spaces $$M^p$$Mp for every $$1\le p\le \infty $$1≤p≤∞, by the membership of its kernel in… read more here.
Keywords: kernel theorems; modulation; theorems modulation; modulation spaces ... See more keywords
Almost Diagonalization of $$\tau $$τ-Pseudodifferential Operators with Symbols in Wiener Amalgam and Modulation Spaces
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Fourier Analysis and Applications"
DOI: 10.1007/s00041-018-09651-z
Abstract: In this paper we focus on the almost-diagonalization properties of $$\tau $$τ-pseudodifferential operators using techniques from time-frequency analysis. Our function spaces are modulation spaces and the special class of Wiener amalgam spaces arising by considering… read more here.
Keywords: diagonalization; modulation spaces; almost diagonalization; wiener amalgam ... See more keywords
The Cauchy Problem for Non-linear Higher Order Hartree Type Equation in Modulation Spaces
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DOI: 10.1007/s00041-018-9629-z
Abstract: We study the Cauchy problem for Hartree equation with cubic convolution nonlinearity $$F(u) = (K \star |u|^{2k})u$$F(u)=(K⋆|u|2k)u under a specified condition on potential K with Cauchy data in modulation spaces $$M^{p,q}(\mathbb {R}^n)$$Mp,q(Rn). We establish global… read more here.
Keywords: modulation spaces; cauchy problem; mathbb; problem non ... See more keywords
Oscillatory hyper-Hilbert transform along curves on modulation spaces
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DOI: 10.1007/s11464-018-0688-x
Abstract: We consider the boundedness of the n-dimension oscillatory hyper-Hilbert transform along homogeneous curves on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces. The main theorems signicantly improve some known results. read more here.
Keywords: modulation; modulation spaces; transform along; hyper hilbert ... See more keywords
Periodic distributions and periodic elements in modulation spaces
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DOI: 10.1016/j.aim.2017.10.040
Abstract: Abstract We characterize periodic elements in Gevrey classes, Gelfand–Shilov distribution spaces and modulation spaces, in terms of estimates of involved Fourier coefficients, and by estimates of their short-time Fourier transforms. If q ∈ [ 1… read more here.
Keywords: modulation spaces; periodic distributions; periodic elements; elements modulation ... See more keywords
Statistically Optimal Estimation of Signals in Modulation Spaces Using Gabor Frames
Sign Up to like & getrecommendations! Published in 2022 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2022.3152734
Abstract: Time-frequency analysis deals with signals for which the underlying spectral characteristics change over time. The essential tool is the short-time Fourier transform, which localizes the Fourier transform in time by means of a window function.… read more here.
Keywords: time; fourier transform; gabor frames; signals modulation ... See more keywords