Principal Value and Its Applications for One Type of Cauchy—Fantappiè Integral and the System of Equations
It is known that principal value plays vital roles in the study of singular integral. In this paper, one type of Cauchy—Fantappiè integral with multiple indexes is introduced. Since the structure of the kernel is complexity, the Jacobian determinant included in the kernel is expanded for making clea...
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| Veröffentlicht in: | Acta mathematica Sinica. English series 2022-09, Vol.38 (9), p.1537-1550 |
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| creator | Chen, Lü Ping |
| description | It is known that principal value plays vital roles in the study of singular integral. In this paper, one type of Cauchy—Fantappiè integral with multiple indexes is introduced. Since the structure of the kernel is complexity, the Jacobian determinant included in the kernel is expanded for making clearly the expression of the kernel. Moreover, one differential operator is utilized for setting up relations between integrals with higher and usual orders. The work also concerns the convergent properties of the integral. In order to study Hadamard principal value and composite formula of this integral, finite and divergent parts will be estimated and separated. As an application, solvability of the system of integral equations with higher order singularity kernel is discussed. |
| doi_str_mv | 10.1007/s10114-022-0590-z |
| format | Article |
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As an application, solvability of the system of integral equations with higher order singularity kernel is discussed.</description><subject>Differential equations</subject><subject>Integral equations</subject><subject>Kernels</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operators (mathematics)</subject><issn>1439-8516</issn><issn>1439-7617</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1kDFOwzAYRiMEEqVwADZLzAH_jmPHY1W1UKlSkSislpM4barUSW1naCcOwSG4BzfhJCQKEhOT_-F9z9ILglvA94Axf3CAAWiICQlxLHB4OgtGQCMRcgb8_PdOYmCXwZVzO4zjjmKjYP9sS5OVjarQm6pajZTJ0cI7NGmaqsyUL2vjUFFbtDIarY-NRnWBpqrNtsfv94-5Ml41Tfn1iRbG643tPL3BbzV6OTqv9z0-O7SD6Dq4KFTl9M3vOw5e57P19Clcrh4X08kyzEAkPkwLioWOOUDGY8ZEHHPGI6YigYkoIipSgISkCvKUYZHkPAGRR0TpnOiCZTQaB3eDt7H1odXOy13dWtN9KQknlCQUU9FRMFCZrZ2zupCNLffKHiVg2VeVQ1XZVZV9VXnqNmTYuI41G23_zP-PfgA8Knuu</recordid><startdate>20220901</startdate><enddate>20220901</enddate><creator>Chen, Lü Ping</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20220901</creationdate><title>Principal Value and Its Applications for One Type of Cauchy—Fantappiè Integral and the System of Equations</title><author>Chen, Lü Ping</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c198t-bf409e5711c756695576736a39029f349b1182ba1db6098d7819d32aed2ef6c43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Differential equations</topic><topic>Integral equations</topic><topic>Kernels</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operators (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Lü Ping</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Acta mathematica Sinica. 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Moreover, one differential operator is utilized for setting up relations between integrals with higher and usual orders. The work also concerns the convergent properties of the integral. In order to study Hadamard principal value and composite formula of this integral, finite and divergent parts will be estimated and separated. As an application, solvability of the system of integral equations with higher order singularity kernel is discussed.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s10114-022-0590-z</doi><tpages>14</tpages></addata></record> |
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| subjects | Differential equations Integral equations Kernels Mathematical analysis Mathematics Mathematics and Statistics Operators (mathematics) |
| title | Principal Value and Its Applications for One Type of Cauchy—Fantappiè Integral and the System of Equations |
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