Zeroes and Isolated Singularities of Analytic Functions

2021 ◽  
pp. 207-246
Author(s):  
J.H. Curtiss
Keyword(s):  
Analytic Functions ◽  
Isolated Singularities

Blow Analytic Mappings and Functions

1993 ◽  
Vol 36 (4) ◽  
pp. 497-506
Author(s):  
Etsuo Yoshinaga
Keyword(s):  
Analytic Functions ◽  
Classical Theorem ◽  
Analytic Family ◽  
Isolated Singularities ◽  
Inverse Mapping ◽  
Continuous Map ◽  
Inverse Mapping Theorem ◽  
Blowing Up ◽  
Analytic Mappings

AbstractLet π: M —> Rn be the blowing-up of Rn at the origin. Then a continuous map-germ f: (Rn — 0,0) —> Rm is called blow analytic if there exists an analytic map-germ such that Then an inverse mapping theorem for blow analytic mappings as a generalization of classical theorem is shown. And the following is shown. Theorem: The analytic family of blow analytic functions with isolated singularities admits an analytic trivialization after blowing-up.

Hyperplane Singularities of Analytic Functions of Several Complex Variables

1997 ◽  
Vol 4 (2) ◽  
pp. 163-184
Author(s):  
M. Shubladze
Keyword(s):  
Critical Points ◽  
Analytic Functions ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Algebraic Expression ◽  
Isolated Singularities ◽  
Milnor Fibre ◽  
New Class

Abstract A new class of non-isolated singularities called hyperplane singularities is introduced. Special deformations with simplest critical points are constructed and an algebraic expression for the number of Morse points is given. The topology of the Milnor fibre is completely studied.

Isolated Singularities of Harmonic Functions and Analytic Functions∗

2001 ◽  
Vol 11 (3) ◽  
pp. 257-272
Author(s):  
Soon-Yeong Chung ◽  
Dohan Kim ◽  
Sang Moon Kim
Keyword(s):  
Analytic Functions ◽  
Harmonic Functions ◽  
Isolated Singularities

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

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