Vector valued fourier series and sample continuity of random processes

1989 ◽  
pp. 375-387 ◽  
Author(s):  
V. I. Tarieladze
Keyword(s):  
Fourier Series ◽  
Random Processes ◽  
Vector Valued

On Haar uniqueness properties for vector-valued random processes

2007 ◽  
Vol 62 (6) ◽  
pp. 1202-1203 ◽  
Author(s):  
V V Gorgorova ◽  
I V Pavlov
Keyword(s):  
Random Processes ◽  
Vector Valued

scholarly journals Deterministic and random approximation by the combination of algebraic polynomials and trigonometric polynomials

2021 ◽  
Vol 19 (1) ◽  
pp. 1047-1055
Author(s):  
Zhihua Zhang
Keyword(s):  
Fourier Series ◽  
Trigonometric Polynomial ◽  
Algebraic Polynomial ◽  
Fourier Coefficients ◽  
Random Processes ◽  
Qualitative Theory ◽  
Trigonometric Polynomials ◽  
Algebraic Polynomials ◽  
Fourier Approximation ◽  
Random Differential Equations

Abstract Fourier approximation plays a key role in qualitative theory of deterministic and random differential equations. In this paper, we will develop a new approximation tool. For an m m -order differentiable function f f on [ 0 , 1 0,1 ], we will construct an m m -degree algebraic polynomial P m {P}_{m} depending on values of f f and its derivatives at ends of [ 0 , 1 0,1 ] such that the Fourier coefficients of R m = f − P m {R}_{m}=f-{P}_{m} decay fast. Since the partial sum of Fourier series R m {R}_{m} is a trigonometric polynomial, we can reconstruct the function f f well by the combination of a polynomial and a trigonometric polynomial. Moreover, we will extend these results to the case of random processes.

A Representation of Vector-Valued Random Processes

1960 ◽  
Vol 39 (1-4) ◽  
pp. 211-216 ◽  
Author(s):  
Edward J. Kelly ◽  
William L. Root
Keyword(s):  
Random Processes ◽  
Vector Valued

Regression Analysis of Vector-Valued Random Processes

1962 ◽  
Vol 10 (1) ◽  
pp. 89-102 ◽  
Author(s):  
W. Freiberger ◽  
M. Rosenblatt ◽  
J. Van Ness
Keyword(s):  
Regression Analysis ◽  
Random Processes ◽  
Vector Valued

scholarly journals On the growth of vector-valued Fourier series

2013 ◽  
Vol 62 (6) ◽  
pp. 1765-1784
Author(s):  
Javier Parcet ◽  
Fernando Soria ◽  
Quanhua Xu
Keyword(s):  
Fourier Series ◽  
Vector Valued

Vector Valued Inequalities for Fourier Series

1980 ◽  
Vol 78 (4) ◽  
pp. 525 ◽  
Author(s):  
Jose L. Rubio De Francia
Keyword(s):  
Fourier Series ◽  
Vector Valued

scholarly journals Pointwise convergence of vector-valued Fourier series

2013 ◽  
Vol 357 (4) ◽  
pp. 1329-1361 ◽  
Author(s):  
Tuomas P. Hytönen ◽  
Michael T. Lacey
Keyword(s):  
Fourier Series ◽  
Pointwise Convergence ◽  
Vector Valued
Sign in / Sign up

Export Citation Format

Share Document