IRIS Uni Torinohttps://iris.unito.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Wed, 27 Jan 2021 07:25:42 GMT2021-01-27T07:25:42Z10651Windowed-Wigner Representations, Interferences and Operatorshttp://hdl.handle.net/2318/131134Titolo: Windowed-Wigner Representations, Interferences and Operators
Abstract: ``Windowed-Wigner'' representations,
denoted by $\Wig_\psi$ and $\Wig_\psi^*$, were introduced in
\cite{BogCarOli2012} in connection with uncertainty principles and
interferences problems. In this paper we present a more precise
analysis of their behavior obtaining an estimate of the $L^2$-norm
of interferences of couples of ``model'' signals. We further define
a suitable functional framework for the associated operators and
show that they form a class of pseudo-differential operators which
define a natural ``path'' between the multiplication, Weyl and
Fourier multipliers operators.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/2318/1311342012-01-01T00:00:00ZNoncommutative Residue for Anisotropic Pseudo-differential Operators in R^nhttp://hdl.handle.net/2318/2265Titolo: Noncommutative Residue for Anisotropic Pseudo-differential Operators in R^n
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/2318/22652003-01-01T00:00:00ZTwo-wavelet Localization Operators on L^p for the Weyl-Heisenberg Grouphttp://hdl.handle.net/2318/103423Titolo: Two-wavelet Localization Operators on L^p for the Weyl-Heisenberg Group
Abstract: The goal of this paper is to investigate the boundedness and compactness on Lp(Rn) of some linear operators that are closely related to Daubechies operators with two admissible wavelets for the Weyl-Heisenberg group . We give two different proofs for the fact that Daubechies operators associated to symbols in L1(Rn × Rn) and two admissible wavelets in
L1(Rn) ∩ L∞(Rn) are bounded linear operators on Lp(Rn), 1 ≤ p ≤ ∞. If the symbols are in Lr(Rn × Rn), 1 ≤ r ≤ 2, and the two admissible wavelets are in L1(Rn) ∩ L2(Rn) ∩ L∞(Rn), then the associated Daubechies operators are proved in Section 3 to be bounded linear operators on Lp(Rn), r ≤ p ≤ r', where r' is the conjugate index of r. The boundedness results in Sections 2 and 3 are then sharpened in Section 4 to results on compactness. Notwithstanding the gain from boundedness to compactness, the boundedness results in Sections 2 and 3 are of interest in their own right because the technique that we use to obtain compactness does not give us explicit estimates for the operator norms of the Daubechies operators in terms of the norms of the symbols and the two admissible wavelets.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/2318/1034232004-01-01T00:00:00ZCohen class of time-frequency representations and operators: boundedness and uncertainty principleshttp://hdl.handle.net/2318/1655943Titolo: Cohen class of time-frequency representations and operators: boundedness and uncertainty principles
Abstract: This paper presents a proof of an uncertainty principle of Donoho-Stark type involving $\varepsilon$-concentration of localization operators. More general operators associated with time-frequency representations in the Cohen class are then considered. For these operators, which include all usual quantizations, we prove a boundedness result in the $L^p$ functional setting and a form of uncertainty principle analogous to that for localization operators.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/2318/16559432018-01-01T00:00:00ZGeneralized Spectrograms and $\tau$-Wigner Transformshttp://hdl.handle.net/2318/61283Titolo: Generalized Spectrograms and $\tau$-Wigner Transforms
Abstract: We consider in this paper Wigner type representations $\Wig_\tau$
depending on a parameter $\tau\in[0,1]$.
We prove that the Cohen class can be characterized in terms of the
convolution of such $\Wig_\tau$ with a tempered distribution. We
introduce furthermore a class of ``quadratic representations''
$\Sp^{\tau}$ based on the $\tau$-Wigner, as an extension of the two
window Spectrogram. We give basic properties of
$\Sp^{\tau}$ as subclasses of the general Cohen
class.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/2318/612832010-01-01T00:00:00ZTwo-window Spectrograms and their Integralshttp://hdl.handle.net/2318/64311Titolo: Two-window Spectrograms and their Integrals
Abstract: We analyze in this paper some basic properties of two-window
spectrograms, introduced in a previous work. This is achieved by the
analysis of their kernel, in view of their immersion in the Cohen
class of time-frequency representations. Further we introduce
weighted averages of two-window spectrograms depending on varying
window functions. We show that these new integrated representations
improve some features of both the classical Rihaczek representation
and the two-window spectrogram which in turns can be viewed as limit
cases of them.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/2318/643112009-01-01T00:00:00ZTime-Frequency Analysis, Modulation Spaces and Localization Operatorshttp://hdl.handle.net/2318/48188Titolo: Time-Frequency Analysis, Modulation Spaces and Localization Operators
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/2318/481882006-01-01T00:00:00ZSchatten Classes for Toeplitz Operators with Hilbert Space Windows on Modulation Spaces.http://hdl.handle.net/2318/25111.2Titolo: Schatten Classes for Toeplitz Operators with Hilbert Space Windows on Modulation Spaces.
Abstract: The aim of this paper is to study Schatten–von Neumann properties of Toeplitz operators with Hilbert windows, acting on Hilbert modulation spaces, i.e. modulation spaces of Hilbert type. Hee and Wong investigated Schatten–von Neumann properties for Toeplitz operators in a powerful way from an abstract point of view. Their results in the general frame of square integrable representations on a Hilbert space are systemized in a some papers which have inspired our work. Actually we shall be especially concerned with various extensions of some of these results. Thereafter we apply our Toeplitz results to prove Young type properties for convolutions between weighted Lebesgue spaces and Schatten–von Neumann classes of symbols in pseudo-differential calculus. Toeplitz operators, or localization operators, appear in the literature in many different situations. They were introduced in time-frequency analysis by Daubechies as certain filters for signals. Lieb and Solovej reformulated problems in quantum mechanics in terms of coherent state transforms, where Toeplitz operators appeared in a natural way. Since then, boundedness and compactness properties of such operators have been investigated in many works. Many of the problems concern Toeplitz operators when acting on Hilbert spaces, especially on L2. In the present paper we consider such questions when the Hilbert spaces are particular classes of modulation spaces and the symbols belong to weighted Lebesgue spaces. Modulation spaces have shown to be a natural class of Banach spaces in certain parts of Fourier analysis, e.g. time-frequency analysis, where the modulation space norms can be used to measure the time-frequency content of signals. At the same time they generalize various Sobolev-type spaces, and in some problems they are appropriate when considering regularity and decay properties of involved functions and distributions. Finally we note that there are many different characterizations available for modulation spaces. For example, they are easy to discretize by means of Gabor frames. In certain situations they can also be characterized in terms of Toeplitz operators. These properties also lead to the fact that modulation spaces have been useful when discussing certain problems of localization operators and pseudo-differential operators, which in some sense can be considered as a part of Fourier Analysis. Actually in the final sections of the paper Schatten–von Neumann symbols of operators acting on Hilbert modulation spaces are used to prove certain composition results for Weyl symbols of trace class characters with analytic functions. In these investigations we use the fact that the Weyl symbol of the Toeplitz operator can be expressed as a convolution between the Toeplitz symbol and a Wigner distribution.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/2318/25111.22008-01-01T00:00:00ZSpectral Asymptotics for Hypoelliptic Operators.http://hdl.handle.net/2318/28071Titolo: Spectral Asymptotics for Hypoelliptic Operators.
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/2318/280711997-01-01T00:00:00ZSobolev Spaces Associated with a Polyhedron and Multiquasielliptic Pseudodifferential Operators in $R^n$.http://hdl.handle.net/2318/26861Titolo: Sobolev Spaces Associated with a Polyhedron and Multiquasielliptic Pseudodifferential Operators in $R^n$.
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/2318/268611993-01-01T00:00:00Z