On the Construction of Regular Solutions for a Class of Generalized Cauchy–Riemann Systems with Coefficients Bounded on the Entire Plane
This article explores the generalized Cauchy–Riemann system on the entire complex plane. The coefficient for the conjugation of the desired function belongs to the H¨older space and, for |z| > 1 , equals eimϕ , where m is an integer. For m ≤ 0 , the system was shown to have no nonzero solutions...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Kazan Federal University
2024-10-01
|
| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://uzakufismat.elpub.ru/jour/article/view/92 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832569210848411648 |
|---|---|
| author | S. Baizaev R. N. Barotov |
| author_facet | S. Baizaev R. N. Barotov |
| author_sort | S. Baizaev |
| collection | DOAJ |
| description | This article explores the generalized Cauchy–Riemann system on the entire complex plane. The coefficient for the conjugation of the desired function belongs to the H¨older space and, for |z| > 1 , equals eimϕ , where m is an integer. For m ≤ 0 , the system was shown to have no nonzero solutions that grow no faster than a polynomial. For m ≥ 0 , the complete set of regular solutions, i.e., those without singularities in the finite part of the plane, was constructed. The obtained solutions were expressed as series of Bessel functions of an imaginary argument. From the resulting set, the solutions bounded on the entire plane were distinguished, and the dimension of the real linear space of these solutions, which equals m , was determined. |
| format | Article |
| id | doaj-art-a855ed81c4a344488e7f99b4e1c43370 |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-a855ed81c4a344488e7f99b4e1c433702025-02-02T23:06:08ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982024-10-01166329730510.26907/2541-7746.2024.3.297-30550On the Construction of Regular Solutions for a Class of Generalized Cauchy–Riemann Systems with Coefficients Bounded on the Entire PlaneS. Baizaev0R. N. Barotov1Tajik State University of Law, Business and PoliticsKhujand State University named after Academician B. GafurovThis article explores the generalized Cauchy–Riemann system on the entire complex plane. The coefficient for the conjugation of the desired function belongs to the H¨older space and, for |z| > 1 , equals eimϕ , where m is an integer. For m ≤ 0 , the system was shown to have no nonzero solutions that grow no faster than a polynomial. For m ≥ 0 , the complete set of regular solutions, i.e., those without singularities in the finite part of the plane, was constructed. The obtained solutions were expressed as series of Bessel functions of an imaginary argument. From the resulting set, the solutions bounded on the entire plane were distinguished, and the dimension of the real linear space of these solutions, which equals m , was determined.https://uzakufismat.elpub.ru/jour/article/view/92generalized cauchy–riemann systemh¨older spacesbounded coefficientsbounded solutions |
| spellingShingle | S. Baizaev R. N. Barotov On the Construction of Regular Solutions for a Class of Generalized Cauchy–Riemann Systems with Coefficients Bounded on the Entire Plane Учёные записки Казанского университета: Серия Физико-математические науки generalized cauchy–riemann system h¨older spaces bounded coefficients bounded solutions |
| title | On the Construction of Regular Solutions for a Class of Generalized Cauchy–Riemann Systems with Coefficients Bounded on the Entire Plane |
| title_full | On the Construction of Regular Solutions for a Class of Generalized Cauchy–Riemann Systems with Coefficients Bounded on the Entire Plane |
| title_fullStr | On the Construction of Regular Solutions for a Class of Generalized Cauchy–Riemann Systems with Coefficients Bounded on the Entire Plane |
| title_full_unstemmed | On the Construction of Regular Solutions for a Class of Generalized Cauchy–Riemann Systems with Coefficients Bounded on the Entire Plane |
| title_short | On the Construction of Regular Solutions for a Class of Generalized Cauchy–Riemann Systems with Coefficients Bounded on the Entire Plane |
| title_sort | on the construction of regular solutions for a class of generalized cauchy riemann systems with coefficients bounded on the entire plane |
| topic | generalized cauchy–riemann system h¨older spaces bounded coefficients bounded solutions |
| url | https://uzakufismat.elpub.ru/jour/article/view/92 |
| work_keys_str_mv | AT sbaizaev ontheconstructionofregularsolutionsforaclassofgeneralizedcauchyriemannsystemswithcoefficientsboundedontheentireplane AT rnbarotov ontheconstructionofregularsolutionsforaclassofgeneralizedcauchyriemannsystemswithcoefficientsboundedontheentireplane |