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

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

scholarly journals Some new function spaces and their applications to Harmonic analysis

1985 ◽  
Vol 62 (2) ◽  
pp. 304-335 ◽  
Author(s):  
R.R Coifman ◽  
Y Meyer ◽  
E.M Stein
Keyword(s):  
Harmonic Analysis ◽  
Function Spaces

scholarly journals The Convergence of Calderón Reproducing Formulae of Two Parameters in $L^p$, in $\mathscr S$ and in $\mathscr S'$

2017 ◽  
Vol 9 (4) ◽  
pp. 87
Author(s):  
Jiang-Wei Huang ◽  
Kunchuan Wang
Keyword(s):  
Harmonic Analysis ◽  
Atomic Decomposition ◽  
Special Function ◽  
Function Spaces ◽  
Approximate Identity ◽  
Single Parameter ◽  
Calderón Reproducing Formula ◽  
The One ◽  
Two Parameters

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 $\mathscr S'(\mathbb R^{n_1} \times \mathbb R^{n_2})$.

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