Decomposition of Spaces of Distributions Induced by Hermite Expansions
نویسندگان
چکیده
Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on R induced by Hermite expansions can be characterized in terms of the needlet coefficients. It is also shown that the Hermite Triebel-Lizorkin and Besov spaces are, in general, different from the respective classical spaces.
منابع مشابه
Bi-Gyrogroup: The Group-Like Structure Induced by Bi-Decomposition of Groups
The decomposition $Gamma=BH$ of a group $Gamma$ into a subset B and a subgroup $H$ of $Gamma$ induces, under general conditions, a group-like structure for B, known as a gyrogroup. The famous concrete realization of a gyrogroup, which motivated the emergence of gyrogroups into the mainstream, is the space of all relativistically admissible velocities along with a binary mbox{...
متن کاملAsymptotic Distributions of Estimators of Eigenvalues and Eigenfunctions in Functional Data
Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...
متن کاملMaximal Operators Associated with Generalized Hermite Polynomial and Function Expansions
We study the weak and strong type boundedness of maximal heat–diffusion operators associated with the system of generalized Hermite polynomials and with two different systems of generalized Hermite functions. We also give a necessary background to define Sobolev spaces in this context.
متن کاملA class of holomorphic Pontryagin spaces and expansions in orthogonal polynomials
We introduce two new classes of holomorphic Pontryagin spaces. Spaces in the first class consist of entire functions and in the second of functions analytic in a disk. These spaces admit reproducing kernels in the form of generalized hypergeometric series and are generalizations of the classical Fischer-Fock and Bergman spaces. In the first part of the paper we obtain representations for the in...
متن کاملAnalysis of Magneto-hydrodynamics Jeffery-Hamel Flow with Nanoparticles by Hermite-Padé Approximation
The combined effects of nanoparticle and magnetic field on the nonlinear Jeffery-Hamel flow are analyzed in the present study. The basic governing equations are solved analytically to nonlinear ordinary differential equation using perturbation method together with a semi-numerical analytical technique called Hermite- Padé approximation. The obtained results are well agreed with that of the Adom...
متن کامل