4 Relative Convolutions . I ∗ . Properties and Applications Vladimir
نویسنده
چکیده
To study operator algebras with symmetries in a wide sense we introduce a notion of relative convolution operators induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already studied (operators of multiplication, usual group convolutions, two-sided convolution etc.) and their different combinations. Basic properties of relative convolutions are given and a connection with usual convolutions is established. Presented examples show that relative convolutions provide us with a base for systematical applications of harmonic analysis to PDO theory, complex and hypercomplex analysis, coherent states, wavelet transform and quantum theory. This work was partially supported by CONACYT Project 1821-E9211, Mexico. On leave from the Odessa State University.
منابع مشابه
ar X iv : f un ct - a n / 94 10 00 1 v 2 5 F eb 2 00 4 RELATIVE CONVOLUTIONS . I PROPERTIES AND APPLICATIONS
To study operator algebras with symmetries in a wide sense we introduce a notion of relative convolution operators induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already studied (operators of multiplication, usual group convolutions, two-sided convolution etc.) and their different combinations. Basic properties of relative convolutio...
متن کاملSome properties of the parametric relative operator entropy
The notion of entropy was introduced by Clausius in 1850, and some of the main steps towards the consolidation of the concept were taken by Boltzmann and Gibbs. Since then several extensions and reformulations have been developed in various disciplines with motivations and applications in different subjects, such as statistical mechanics, information theory, and dynamical systems. Fujii and Kam...
متن کاملImplicitly Dealiased Convolutions: Example Applications and Performance Comparison
Implicitly dealiasing is a recently-developed technique which improves upon conventional zero padding to compute linear convolutions via fast Fourier transforms. For onedimensional inputs, the memory requirements and performance are similar to conventional zero-padded convolutions, but implicitly dealiased convolutions are faster and require less memory when the data is multi-dimensional. We sh...
متن کاملSchur properties of convolutions of gamma random variables
Sufficient conditions for comparing the convolutions of heterogeneousgamma random variables in terms of the usual stochastic order are established.Such comparisons are characterized by the Schur convexity properties of thecumulative distribution function of the convolutions. Some examples of thepractical applications of our results are given.
متن کاملGeometric Convolutions and Fourier Restriction beyond Curves and Hypersurfaces
I will present recent results relating to two problems in Fourier analysis, L-improving properties of convolutions with singular measures and the Fourier restriction problem, both of which deal with the analysis of operators associated to submanifolds of Euclidean space. In both cases the theory is much more welldeveloped for curves and hypersurfaces than it is for submanifolds of intermediate ...
متن کامل