Choosing Function Spaces in Harmonic Analysis

The Calderón reproducing formula is the most important in the study of harmonic analysis, which has the same property as the one of approximate identity in many special function spaces. In this note, we use the idea of separation variables and atomic decomposition to extend single parameter to two-parameters and discuss the convergence of Calderón reproducing formulae of two-parameters in $L^p(\mathbb R^{n_1} \times \mathbb R^{n_2})$, in $\mathscr S(\mathbb R^{n_1} \times \mathbb R^{n_2})$ and in $\mathscr S'(\mathbb R^{n_1} \times \mathbb R^{n_2})$.

Download Full-text

Finding Invariants of Group Actions on Function Spaces, a General Methodology from Non-Abelian Harmonic Analysis

Mathematical Control Theory and Finance ◽

10.1007/978-3-540-69532-5_10 ◽

2008 ◽

pp. 161-186

Author(s):

Jean-Paul Gauthier ◽

Fethi Smach ◽

Cedric Lemaître ◽

Johel Miteran

Keyword(s):

Harmonic Analysis ◽

Group Actions ◽

Function Spaces ◽

General Methodology

Download Full-text

Harmonic Analysis Methods for Function Spaces, Differential Equations and Data Science

Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science - Applied and Numerical Harmonic Analysis ◽

10.1007/978-3-319-55556-0_1 ◽

2017 ◽

pp. 441-447

Author(s):

Isaac Pesenson

Keyword(s):

Differential Equations ◽

Harmonic Analysis ◽

Data Science ◽

Function Spaces ◽

Analysis Methods

Download Full-text

Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L2 metric: Nikol'skii–Besov type function spaces

Integral Transforms and Special Functions ◽

10.1080/10652469.2019.1691548 ◽

2019 ◽

Vol 31 (4) ◽

pp. 281-298

Author(s):

S. S. Platonov

Keyword(s):

Harmonic Analysis ◽

Function Spaces ◽

Approximation Of Functions ◽

Type Function ◽

Half Axis

Download Full-text

Characterization of lipschitz spaces on compact Lie groups

Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics ◽

10.1017/s1446788700038234 ◽

1995 ◽

Vol 58 (2) ◽

pp. 200-209

Author(s):

Dashan Fan ◽

Zengfu Xu

Keyword(s):

Harmonic Analysis ◽

Lie Groups ◽

Function Spaces ◽

The Other ◽

Euclidean Spaces ◽

Compact Lie Groups ◽

Lipschitz Spaces

AbstractLipschitz spaces are important function spaces with relations to Hp spaces and Campanato spaces, the other two important function spaces in harmonic analysis. In this paper we give some characterizations for Lipschitz spaces on compact Lie groups, which are analogues of results in Euclidean spaces.

Download Full-text