arXiv subjects

F. Gómez-Cubillo

Publications and source records attributed to F. Gómez-Cubillo.

5 recordsLinked to original sources

arXiv2019

Admissible vectors and Hilbert algebras

Admissible vectors for unitary representations of locally compact groups are the basis for group-frame and covariant coherent state expansions. Main tools in the study of admissible vectors have been Plancherel and central integral decomposition, of applicability only under certain separability and semifiniteness restrictions. In this work we present a study of admissible vectors in terms of convolution Hilbert algebras valid for arbitrary unitary representations of general locally compact groups.

math.FA↗

arXiv2019

Wavelet frames: Spectral techniques and extension principles

This work characterizes (dyadic) wavelet frames for $L^2({\mathbb R})$ by means of spectral techniques. These techniques use decomposability properties of the frame operator in spectral representations associated to the dilation operator. The approach is closely related to usual Fourier domain fiberization techniques, dual Gramian analysis and extension principles, which are described here on the basis of the periodized Fourier transform. In a second paper of this series, we shall show how the spectral formulas obtained here permit us to calculate all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed number of generators of minimal support.

math.FA↗

arXiv2019

Univariate tight wavelet frames of minimal support

Wavelet frames for $L^2({\mathbb R})$ can be characterized by means of spectral techniques. This work uses spectral formulas to determine all the tight wavelet frames for $L^2({\mathbb R})$ with a fixed finite number of generators of minimal support. The method associates wavelet frames of this type with certain inner operator-valued functions in Hardy spaces. The cases with one and two generators are completely solved.

math.FA↗

arXiv2013

Point-form dynamics of quasistable states

We present a field theoretical model of point-form dynamics which exhibits resonance scattering. In particular, we construct point-form Poincaré generators explicitly from field operators and show that in the vector spaces for the in-states and out-states (endowed with certain analyticity and topological properties suggested by the structure of the $S$-matrix) these operators integrate to furnish differentiable representations of the causal Poincaré semigroup, the semidirect product of the semigroup of spacetime translations into the forward lightcone and the group of Lorentz transformations. We also show that there exists a class of \emph{irreducible} representations of the Poincaré semigroup defined by a complex mass and a half-integer spin. The complex mass characterizing the representation naturally appears in the construction as the square root of the pole position of the propagator. These representations provide a description of resonances in the same vein as Wigner's unitary irreducible representations of the Poincaré group provide a description of stable particles.

math-ph↗

arXiv2009

Spectral Models for Orthonormal Wavelets and Multiresolution Analysis of $L^2({\mathbb R})$

Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions defined on the functional spectral spaces. The approach is useful for computational purposes.

math.FA↗