On value regions of analytic functions represented by a Stieltjes integral

1962 ◽  
pp. 81-94
Author(s):  
I. Ja. Ašnevic ◽  
G. V. Ulina
Keyword(s):  
Analytic Functions ◽  
Stieltjes Integral

Multiplicative Integration of Infinite Products

1971 ◽  
Vol 23 (4) ◽  
pp. 692-698 ◽  
Author(s):  
David Lowell Lovelady
Keyword(s):  
Integral Equation ◽  
Abelian Group ◽  
Analytic Functions ◽  
Stieltjes Integral ◽  
Real Numbers ◽  
Main Result Theorem ◽  
Infinite Products ◽  
Product Integral ◽  
Result Theorem ◽  
Image Position

Let G be a complete normed abelian group with norm N1. Let S be an interval (bounded or otherwise) of real numbers. We propose to study the Stieltjes integral equationwhere p is in G, a is in S, and each Fk is a function on S each value of which is a function from G to G. Our primary tools of investigation will be the works of J. S. MacNerney [6; 7] and their extensions by the author [4; 5]. Our main result, Theorem 4, will show that the equation above can be solved by a product integral of infinite products of solutions for the summands of the integrator. After obtaining our results, we shall specialize them to a linear situation and then show how this specialization allows us to obtain representations for analytic functions having only invertible values in a complex Banach algebra with identity.

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.

A NEW SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY OPOOLA DIFFERENTIAL OPERATOR

2020 ◽  
Vol 9 (8) ◽  
pp. 5343-5348 ◽  
Author(s):  
T. G. Shaba ◽  
A. A. Ibrahim ◽  
M. F. Oyedotun
Keyword(s):  
Differential Operator ◽  
Analytic Functions
Sign in / Sign up

Export Citation Format

Share Document