On the symbol of singular operators in the case of contour with corner points
This paper proposes a method for constructing a symbol for singular integral operators in the case of a piecewise Lyapunov contour. The definition of the symbol function involves numbers that characterize the space in which the research is being carried out, as well as the values of the corner poin...
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| Format: | Article |
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"Ion Creanga" State Pedagogical University
2025-01-01
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| Series: | Acta et Commentationes: Ştiinţe Exacte şi ale Naturii |
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| Online Access: | https://revistaust.upsc.md/index.php/acta_exacte/article/view/1086 |
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| _version_ | 1823857440568901632 |
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| author | Vasile Neagu Petru Moloșnic |
| author_facet | Vasile Neagu Petru Moloșnic |
| author_sort | Vasile Neagu |
| collection | DOAJ |
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This paper proposes a method for constructing a symbol for singular integral operators in the case of a piecewise Lyapunov contour. The definition of the symbol function involves numbers that characterize the space in which the research is being carried out, as well as the values of the corner points of the contour, which makes it possible to obtain formulas for calculating the essential norms of singular operators and conditions for the solvability of singular equations with a shift and complex conjugation. In obtaining these results, we will essentially rely on the well-known results of I. Gelfand concerning maximal ideals of commutative Banach algebras \cite{GRS}. In the absence of corner points on the integration contour, the results of this work are consistent with the results from [1].
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| format | Article |
| id | doaj-art-9b5a916c211943e88e1bd265f1391a97 |
| institution | Kabale University |
| issn | 2537-6284 2587-3644 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | "Ion Creanga" State Pedagogical University |
| record_format | Article |
| series | Acta et Commentationes: Ştiinţe Exacte şi ale Naturii |
| spelling | doaj-art-9b5a916c211943e88e1bd265f1391a972025-02-11T21:03:57Zeng"Ion Creanga" State Pedagogical UniversityActa et Commentationes: Ştiinţe Exacte şi ale Naturii2537-62842587-36442025-01-0118210.36120/2587-3644.v18i2.55-69On the symbol of singular operators in the case of contour with corner pointsVasile Neagu0Petru Moloșnic1``Ion Creanga'' State Pedagogical University, 1 Ion Creanga st., Chisinau, Republic of MoldovaTechnical University of Moldova, 9/8 Studentilor St., Chisinau, Republic of Moldova This paper proposes a method for constructing a symbol for singular integral operators in the case of a piecewise Lyapunov contour. The definition of the symbol function involves numbers that characterize the space in which the research is being carried out, as well as the values of the corner points of the contour, which makes it possible to obtain formulas for calculating the essential norms of singular operators and conditions for the solvability of singular equations with a shift and complex conjugation. In obtaining these results, we will essentially rely on the well-known results of I. Gelfand concerning maximal ideals of commutative Banach algebras \cite{GRS}. In the absence of corner points on the integration contour, the results of this work are consistent with the results from [1]. https://revistaust.upsc.md/index.php/acta_exacte/article/view/1086singular operatorBanach algebraspiecewise Lyapunov contoursymbolNoether conditions |
| spellingShingle | Vasile Neagu Petru Moloșnic On the symbol of singular operators in the case of contour with corner points Acta et Commentationes: Ştiinţe Exacte şi ale Naturii singular operator Banach algebras piecewise Lyapunov contour symbol Noether conditions |
| title | On the symbol of singular operators in the case of contour with corner points |
| title_full | On the symbol of singular operators in the case of contour with corner points |
| title_fullStr | On the symbol of singular operators in the case of contour with corner points |
| title_full_unstemmed | On the symbol of singular operators in the case of contour with corner points |
| title_short | On the symbol of singular operators in the case of contour with corner points |
| title_sort | on the symbol of singular operators in the case of contour with corner points |
| topic | singular operator Banach algebras piecewise Lyapunov contour symbol Noether conditions |
| url | https://revistaust.upsc.md/index.php/acta_exacte/article/view/1086 |
| work_keys_str_mv | AT vasileneagu onthesymbolofsingularoperatorsinthecaseofcontourwithcornerpoints AT petrumolosnic onthesymbolofsingularoperatorsinthecaseofcontourwithcornerpoints |