A convolution product for discrete function theory

1964 ◽  
Vol 31 (2) ◽  
pp. 199-220 ◽  
Author(s):  
R. J. Duffin ◽  
C. S. Duris
Keyword(s):  
Function Theory ◽  
Convolution Product ◽  
Discrete Function ◽  
Discrete Function Theory

scholarly journals Discrete Hardy Spaces for Bounded Domains in $${\mathbb {R}}^{n}$$

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Paula Cerejeiras ◽  
Uwe Kähler ◽  
Anastasiia Legatiuk ◽  
Dmitrii Legatiuk
Keyword(s):  
Half Space ◽  
Hardy Spaces ◽  
Function Theory ◽  
Bounded Domains ◽  
Discrete Function ◽  
Higher Dimensional ◽  
Stokes Formula ◽  
Discrete Function Theory ◽  
Discrete Hardy Spaces ◽  
Discrete Setting

AbstractDiscrete function theory in higher-dimensional setting has been in active development since many years. However, available results focus on studying discrete setting for such canonical domains as half-space, while the case of bounded domains generally remained unconsidered. Therefore, this paper presents the extension of the higher-dimensional function theory to the case of arbitrary bounded domains in $${\mathbb {R}}^{n}$$ R n . On this way, discrete Stokes’ formula, discrete Borel–Pompeiu formula, as well as discrete Hardy spaces for general bounded domains are constructed. Finally, several discrete Hilbert problems are considered.

scholarly journals Discrete function theory based on skew Weyl relations

2010 ◽  
Vol 138 (09) ◽  
pp. 3241-3241 ◽  
Author(s):  
Hilde De Ridder ◽  
Hennie De Schepper ◽  
Uwe Kähler ◽  
Frank Sommen
Keyword(s):  
Function Theory ◽  
Discrete Function ◽  
Discrete Function Theory

scholarly journals Certain results on q-starlike and q-convex error functions

2018 ◽  
Vol 68 (2) ◽  
pp. 361-368 ◽  
Author(s):  
C. Ramachandran ◽  
L. Vanitha ◽  
Stanisłava Kanas
Keyword(s):  
Future Study ◽  
Difference Operator ◽  
Function Theory ◽  
Error Function ◽  
Complex Function ◽  
Mathematical Physics ◽  
Natural Sciences ◽  
Convolution Product ◽  
Complex Function Theory ◽  
The Past

Abstract The error function occurs widely in multiple areas of mathematics, mathematical physics and natural sciences. There has been no work in this area for the past four decades. In this article, we estimate the coefficient bounds with q-difference operator for certain classes of the spirallike starlike and convex error function associated with convolution product using subordination as well as quasi-subordination. Though this concept is an untrodden path in the field of complex function theory, it will prove to be an encouraging future study for researchers on error function.

Brownian motion with quadratic killing and some implications

1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur
Keyword(s):  
Brownian Motion ◽  
Weibull Distribution ◽  
Special Function ◽  
Function Theory ◽  
Killing Rate

Brownian motion subject to a quadratic killing rate and its connection with the Weibull distribution is analyzed. The distribution obtained for the process killing time significantly generalizes the Weibull. The derivation involves the use of the Karhunen–Loève expansion for Brownian motion, special function theory, and the calculus of residues.

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