On a Class of A-Analytic Functions

Jabborov, Nasridin M.; Sadullaev, Azimbay; Жабборов, Насридин М.

doi:10.17516/1997-1397-2016-9-3-374-383

Cited by 9 publications

(5 citation statements)

References 1 publication

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“…converges uniformly on ∂L(a, r), then we can substitute (14) into the integral (13) and interchange the sum and the integral: Similarly, we can prove∂…”

Section: Functional Seriesmentioning

confidence: 91%

“…(see[14]). If f (z) ∈ O A (L(a, r)),where L(a, r) = {ξ ∈ D : |ψ(ξ, a)| < r} D is a lemniscate, then the function f (z) can be expanded into the series in L(a, r): f (z) = ∞ ∑ k=0 c k ψ k (z, a).…”

mentioning

confidence: 99%

“…Theorem 4.3 (Laurent series expansion, see [14]). Let f (z) be A-analytic in a ring of lemniscates: f ∈ O A (L(a, R)\L(a, r)), r < R. Then f (z) admits a 'Laurent' series expansion in this ring:…”

mentioning

confidence: 99%

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Morera’s Theorem and Functional Series in the Class of A-analytic Functions

Jabborov¹,

Жабборов²

2018

J. Sib. Fed. Univ., Math. phys.

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The aim of this paper is to investigate A-analytic functions in a special case when the function A is an anti-analytic function in a domain. We prove that a continuous function satisfying the integral condition of the Cauchy theorem is A-analytic (an analog of Morera's theorem, Sec. 2). In Sec. 3 we prove an analog of the Weierstrass theorem for functional series of A-analytic functions and the expansion of A-analytic functions into functional series (Sec. 4).

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“…converges uniformly on ∂L(a, r), then we can substitute (14) into the integral (13) and interchange the sum and the integral: Similarly, we can prove∂…”

Section: Functional Seriesmentioning

confidence: 91%

mentioning

confidence: 99%

See 1 more Smart Citation

Morera’s Theorem and Functional Series in the Class of A-analytic Functions

Jabborov¹,

Жабборов²

2018

J. Sib. Fed. Univ., Math. phys.

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“…The Beltrami equation was generalized in [1] to the case where 𝑤(𝑧) is a vector-valued function and 𝐴(𝑧) is a linear operator in the corresponding vector space. The methodological advances discovered in [6] for obtaining analogues of classical results were used in [7] for the usual Beltrami equation ( ) ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ = 𝐴(𝑧).…”

Section: Introductionmentioning

confidence: 99%

Compactness of the Family of A(z)-Analytic Functions

Radhi,

Lyan

2023

Al-Mustansiriyah Journal of Science

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In recent years, the Beltrami equation has garnered the attention of numerous researchers for the study of its analytical properties. Therefore, in this paper, we investigate certain properties of an analogue of the Cauchy integral for A(z)-analytic functions, utilizing the analytical properties of the Beltrami equation. Additionally, we obtain the compactness conditions for a family of functions within an A(z)-lemniscate.

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“…According to ( 1 ) the A (z)-Class Analytic Function f (z) ∈ ( ) is It is distinguished as a result of (z) = 0.…”

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confidence: 99%