A convolution product for discrete function theory

1964 ◽  
Vol 31 (2) ◽  
pp. 199-220 ◽  
Author(s):  
R. J. Duffin ◽  
C. S. Duris
2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Paula Cerejeiras ◽  
Uwe Kähler ◽  
Anastasiia Legatiuk ◽  
Dmitrii Legatiuk

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.


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

2018 ◽  
Vol 68 (2) ◽  
pp. 361-368 ◽  
Author(s):  
C. Ramachandran ◽  
L. Vanitha ◽  
Stanisłava Kanas

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.


1986 ◽  
Vol 23 (04) ◽  
pp. 893-903 ◽  
Author(s):  
Michael L. Wenocur

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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