Analytic Riemann boundary value problem on h-summable closed curves

Ricardo Abreu Blaya; Juan Bory Reyes; Tania Moreno García; Yudier Peña Pérez

doi:10.1016/j.amc.2013.11.053

Analytic Riemann boundary value problem on h-summable closed curves

Ricardo Abreu Blaya, Juan Bory Reyes, Tania Moreno García, Yudier Peña Pérez

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

The aim of this work is to further extend the notion of d-summability due to Harrison and Norton in the beginning of the 1990s. Explicit examples are given to illustrate how our notion can be applied to describe the geometry of a simply connected bounded open subset of C in a more delicate manner than the latter one. Applications on the solvability conditions for the Riemann boundary value problems for analytic functions over closed curves merely required to be summable in the generalized sense are described.

Original language	English
Pages (from-to)	593-600
Number of pages	8
Journal	Applied Mathematics and Computation
Volume	227
DOIs	https://doi.org/10.1016/j.amc.2013.11.053
State	Published - 15 Jan 2014
Externally published	Yes

Keywords

Analytic functions
Fractal dimensions
Riemann boundary value problem

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10.1016/j.amc.2013.11.053

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abstract = "The aim of this work is to further extend the notion of d-summability due to Harrison and Norton in the beginning of the 1990s. Explicit examples are given to illustrate how our notion can be applied to describe the geometry of a simply connected bounded open subset of C in a more delicate manner than the latter one. Applications on the solvability conditions for the Riemann boundary value problems for analytic functions over closed curves merely required to be summable in the generalized sense are described.",

keywords = "Analytic functions, Fractal dimensions, Riemann boundary value problem",

author = "Blaya, {Ricardo Abreu} and Reyes, {Juan Bory} and Garc{\'i}a, {Tania Moreno} and P{\'e}rez, {Yudier Pe{\~n}a}",

note = "Funding Information: This research was partly supported by CAPES/MES-CUBA programs, Project 151/12 and much of the work completed during a stay of the first author at IMPA, Rio de Janeiro. The kind hospitality is gratefully acknowledged. ",

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AU - Blaya, Ricardo Abreu

AU - Reyes, Juan Bory

AU - García, Tania Moreno

AU - Pérez, Yudier Peña

N1 - Funding Information: This research was partly supported by CAPES/MES-CUBA programs, Project 151/12 and much of the work completed during a stay of the first author at IMPA, Rio de Janeiro. The kind hospitality is gratefully acknowledged.

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N2 - The aim of this work is to further extend the notion of d-summability due to Harrison and Norton in the beginning of the 1990s. Explicit examples are given to illustrate how our notion can be applied to describe the geometry of a simply connected bounded open subset of C in a more delicate manner than the latter one. Applications on the solvability conditions for the Riemann boundary value problems for analytic functions over closed curves merely required to be summable in the generalized sense are described.

AB - The aim of this work is to further extend the notion of d-summability due to Harrison and Norton in the beginning of the 1990s. Explicit examples are given to illustrate how our notion can be applied to describe the geometry of a simply connected bounded open subset of C in a more delicate manner than the latter one. Applications on the solvability conditions for the Riemann boundary value problems for analytic functions over closed curves merely required to be summable in the generalized sense are described.

KW - Analytic functions

KW - Fractal dimensions

KW - Riemann boundary value problem

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VL - 227

SP - 593

EP - 600

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

Analytic Riemann boundary value problem on h-summable closed curves

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Keywords

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