Riemann boundary value problems on the positive real axis

2017 ◽  
Vol 47 (8) ◽  
pp. 887-918
Author(s):  
DU JinYuan ◽  
DUAN Ping ◽  
WANG Ying
Keyword(s):  
Boundary Value Problems ◽  
Real Axis ◽  
Boundary Value ◽  
Positive Real Axis ◽  
Positive Real ◽  
Riemann Boundary

scholarly journals An Extension of the Almost Isolated Singularity of Finite Exponential Order

1964 ◽  
Vol 14 (2) ◽  
pp. 137-141
Author(s):  
R. Wilson
Keyword(s):  
Real Axis ◽  
Taylor Series ◽  
Positive Real Axis ◽  
Isolated Singularity ◽  
Positive Real ◽  
Small Disk ◽  
Exponential Order ◽  
Disk Centre ◽  
Image Position

Let f(z) be represented on its circle of convergence |z| = 1 by the Taylor seriesand suppose that its sole singularity on |z| = 1 is an almost isolated singularity at z = 1. In the neighbourhood of such a singularity f(z) is regular on a sufficiently small disk, centre z = 1, with the outward drawn radius along the positive real axis excised. If also in this neighbourhood |f(z)| e−(1/δ)ρ remains bounded for some finite ρ, where δ is the distance from the excised radius, then the singularity is said to be of finite exponential order.

scholarly journals Markov chains with quasitoeplitz transition matrix: first zero hitting

1989 ◽  
Vol 2 (3) ◽  
pp. 205-216
Author(s):  
Alexander M. Dukhovny
Keyword(s):  
Markov Chains ◽  
Boundary Value Problems ◽  
Unit Circle ◽  
Generating Functions ◽  
Transition Matrix ◽  
Boundary Value ◽  
Riemann Boundary ◽  
Hitting Probabilities

This paper continues the investigation of Markov Chains with a quasitoeplitz transition matrix. Generating functions of first zero hitting probabilities and mean times are found by the solution of special Riemann boundary value problems on the unit circle. Duality is discussed.

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