scholarly journals Validity of Closed Ideals in Algebras of Series of Square Analytic Functions

2019 ◽  
Vol 4 (2) ◽  
pp. 51-64
Author(s):  
Musa Siddig ◽  
Shawgy Hussien
Keyword(s):  
Lipschitz Condition ◽  
Analytic Functions

We show the validity of a complete description of closed ideals of the algebra is the algebra of series of analytic functions satisfying the Lipschitz condition of order αj2 obtained by.15

scholarly journals Closed Ideals in Some Algebras of Analytic Functions

2009 ◽  
Vol 61 (2) ◽  
pp. 282-298 ◽  
Author(s):  
Brahim Bouya
Keyword(s):  
Lipschitz Condition ◽  
Analytic Functions ◽  
Dirichlet Space

Abstract. We obtain a complete description of closed ideals of the algebra 𝒟 ∩lipα, 0 < α ≤ ½ , where 𝒟 is the Dirichlet space and lipα is the algebra of analytic functions satisfying the Lipschitz condition of order α.

Titchmarsh's theorem of Hankel transform

2019 ◽  
pp. 11-24
Author(s):  
Mohamed-Ahmed Boudref
Keyword(s):  
Number Theory ◽  
Data Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Analytic Number Theory ◽  
Hankel Transform ◽  
Partial Differential ◽  
Analytic Number ◽  
Bessel Transform

Hankel transform (or Fourier-Bessel transform) is a fundamental tool in many areas of mathematics and engineering, including analysis, partial differential equations, probability, analytic number theory, data analysis, etc. In this article, we prove an analog of Titchmarsh's theorem for the Hankel transform of functions satisfying the Hankel-Lipschitz condition.

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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