1,721,029 research outputs found
Defensa social : la prevencion a priori : Venezuela
No full textSeminário sobre planejamento da defesa social dentro dos programas do desenvolvimento na América Latina.Maria Elena Cordero de Gord
Sharp integral bounds for Wigner distributions
Full text linkThe cross-Wigner distribution of two functions or temperate
distributions is a fundamental tool in quantum mechanics and in signal
analysis. Usually, in applications in time-frequency analysis and
belong to some modulation space and it is important to know which modulation
spaces belongs to. Although several particular sufficient conditions
have been appeared in this connection, the general problem remains open. In the
present paper we solve completely this issue by providing the full range of
modulation spaces in which the continuity of the cross-Wigner distribution
holds, as a function of . The case of weighted modulation spaces
is also considered. The consequences of our results are manifold: new bounds
for the short-time Fourier transform and the ambiguity function, boundedness
results for pseudodifferential (in particular, localization) operators and
properties of the Cohen class
Exponentially sparse representations of Fourier integral operators
No full textWe investigate the sparsity of the Gabor-matrix representation of Fourier integral operators with a phase having quadratic growth. It is known that such an infinite matrix is sparse and well organized, being in fact concentrated along the graph of the corresponding canonical transformation. Here we show that, if the phase and symbol have a regularity of Gevrey type of order s>1 or analytic (s=1), the above decay is in fact sub-exponential or exponential, respectively. We also show by a counterexample that ultra-analytic regularity (s<1) does not give super-exponential decay. This is in sharp contrast to the more favorable case of pseudodifferential operators, or even (generalized) metaplectic operators, which are treated as well
Symplectic analysis of time-frequency spaces
Full text linkWe present a different symplectic point of view in the definition of weighted modulation spaces and weighted Wiener amalgam spaces. All the classical time-frequency representations, such as the short-time Fourier transform (STFT), the τ-Wigner distributions and the ambiguity function, can be written as metaplectic Wigner distributions \mu(A)(f\otimes\bar g), where \mu(A) is the metaplectic operator and A is the associated symplectic matrix. Namely, time-frequency representations can be represented as images of metaplectic operators, which become the real protagonists of time-frequency analysis. In [13], the authors suggest that any metaplectic Wigner distribution that satisfies the so-called shift-invertibility condition can replace the STFT in the definition of modulation spaces. In this work, we prove that shift-invertibility alone is not sufficient, but it has to be complemented by an upper-triangularity condition for this characterization to hold, whereas a lower-triangularity property comes into play for Wiener amalgam spaces. The shift-invertibility property is necessary: Rihaczek and conjugate Rihaczek distributions are not shift-invertible and they fail the characterization of the above spaces. We also exhibit examples of shift-invertible distributions without upper-triangularity condition which do not define modulation spaces. Finally, we provide new families of time-frequency representations that characterize modulation spaces, with the purpose of replacing the time-frequency shifts with other atoms that allow to decompose signals differently, with possible new outcomes in applications
Quasi-Banach algebras and Wiener properties for pseudodifferential and generalized metaplectic operators
Full text linkWe generalize the results for Banach algebras of pseudodifferential operators
obtained by Gr\"ochenig and Rzeszotnik in [24] to quasi-algebras of Fourier
integral operators. Namely, we introduce quasi-Banach algebras of symbol
classes for Fourier integral operators that we call generalized metaplectic
operators, including pseudodifferential operators. This terminology stems from
the pioneering work on Wiener algebras of Fourier integral operators [11],
which we generalize to our framework. This theory finds applications in the
study of evolution equations such as the Cauchy problem for the Schr\"odinger
equation with bounded perturbations, cf. [7].Comment: 26 page
Time-frequency Analysis of Born-Jordan Pseudodifferential Operators
No full textBorn-Jordan operators are a class of pseudodifferential operators arising as a generalization of the quantization rule for polynomials on the phase space introduced by Born and Jordan in 1925. The weak definition of such operators involves the Born-Jordan distribution, first introduced by Cohen in 1966 as a member of the Cohen class. We perform a time-frequency analysis of the Cohen kernel of the Born -Jordan distribution, using modulation and Wiener amalgam spaces. We then provide sufficient and necessary conditions for Born-Jordan operators to be bounded on modulation spaces. We use modulation spaces as appropriate symbols classes
Wiener algebras of Fourier integral operators
Full text linkAbstractWe construct a one-parameter family of algebras FIO(Ξ,s), 0⩽s⩽∞, consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of the operators in FIO(Ξ,s). The operator algebra is defined by the decay properties of an associated Gabor matrix around the graph of the canonical transformation. In particular, for the limit case s=∞, our Gabor technique provides a new approach to the analysis of S0,00-type Fourier integral operators, for which the global calculus represents a still open relevant problem
Wigner analysis of fourier integral operators with symbols in the Shubin classes
Full text linkWe study the decay properties of Wigner kernels for Fourier integral operators of types I and II. The symbol spaces that allow a nice decay of these kernels are the Shubin classes with negative order m. The phases considered are the so-called tame ones, which appear in the Schrödinger propagators. The related canonical transformations are allowed to be nonlinear. It is the nonlinearity of these transformations that are the main obstacles for nice kernel localizations when symbols are taken in the Hörmander’s class. Here we prove that Shubin classes overcome this problem and allow a nice kernel localization, which improves with the decreasing of the order m
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