Analysis IV: Linear and Boundary Integral Equations
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1991
|
| Series: | Encyclopaedia of Mathematical Sciences
27 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | A linear integral equation is an equation of the form XEX. (1) 2a(x)cp(x) - Ix k(x, y)cp(y)dv(y) = f(x), Here (X, v) is a measure space with a-finite measure v, 2 is a complex parameter, and a, k, f are given (complex-valued) functions, which are referred to as the coefficient, the kernel, and the free term (or the right-hand side) of equation (1), respectively. The problem consists in determining the parameter 2 and the unknown function cp such that equation (1) is satisfied for almost all x E X (or even for all x E X if, for instance, the integral is understood in the sense of Riemann). In the case f = 0, the equation (1) is called homogeneous, otherwise it is called inhomogeneous. If a and k are matrix functions and, accordingly, cp and f are vector-valued functions, then (1) is referred to as a system of integral equations. Integral equations of the form (1) arise in connection with many boundary value and eigenvalue problems of mathematical physics. Three types of linear integral equations are distinguished: If 2 = 0, then (1) is called an equation of the first kind; if 2a(x) i= 0 for all x E X, then (1) is termed an equation of the second kind; and finally, if a vanishes on some subset of X but 2 i= 0, then (1) is said to be of the third kind |
| Physical Description: | 1 Online-Ressource (VII, 236 p) |
| ISBN: | 9783642581755 9783642634918 |
| ISSN: | 0938-0396 |
| DOI: | 10.1007/978-3-642-58175-5 |
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| 245 | 1 | 0 | |a Analysis IV |b Linear and Boundary Integral Equations |c edited by V. G. Maz’ya, S. M. Nikol’skiĭ |
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| 500 | |a A linear integral equation is an equation of the form XEX. (1) 2a(x)cp(x) - Ix k(x, y)cp(y)dv(y) = f(x), Here (X, v) is a measure space with a-finite measure v, 2 is a complex parameter, and a, k, f are given (complex-valued) functions, which are referred to as the coefficient, the kernel, and the free term (or the right-hand side) of equation (1), respectively. The problem consists in determining the parameter 2 and the unknown function cp such that equation (1) is satisfied for almost all x E X (or even for all x E X if, for instance, the integral is understood in the sense of Riemann). In the case f = 0, the equation (1) is called homogeneous, otherwise it is called inhomogeneous. If a and k are matrix functions and, accordingly, cp and f are vector-valued functions, then (1) is referred to as a system of integral equations. Integral equations of the form (1) arise in connection with many boundary value and eigenvalue problems of mathematical physics. Three types of linear integral equations are distinguished: If 2 = 0, then (1) is called an equation of the first kind; if 2a(x) i= 0 for all x E X, then (1) is termed an equation of the second kind; and finally, if a vanishes on some subset of X but 2 i= 0, then (1) is said to be of the third kind | ||
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Record in the Search Index
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| id | DE-604.BV042422716 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642581755 9783642634918 |
| issn | 0938-0396 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858133 |
| oclc_num | 863705138 |
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| physical | 1 Online-Ressource (VII, 236 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Encyclopaedia of Mathematical Sciences |
| spelling | Maz’ya, V. G. Verfasser aut Analysis IV Linear and Boundary Integral Equations edited by V. G. Maz’ya, S. M. Nikol’skiĭ Berlin, Heidelberg Springer Berlin Heidelberg 1991 1 Online-Ressource (VII, 236 p) txt rdacontent c rdamedia cr rdacarrier Encyclopaedia of Mathematical Sciences 27 0938-0396 A linear integral equation is an equation of the form XEX. (1) 2a(x)cp(x) - Ix k(x, y)cp(y)dv(y) = f(x), Here (X, v) is a measure space with a-finite measure v, 2 is a complex parameter, and a, k, f are given (complex-valued) functions, which are referred to as the coefficient, the kernel, and the free term (or the right-hand side) of equation (1), respectively. The problem consists in determining the parameter 2 and the unknown function cp such that equation (1) is satisfied for almost all x E X (or even for all x E X if, for instance, the integral is understood in the sense of Riemann). In the case f = 0, the equation (1) is called homogeneous, otherwise it is called inhomogeneous. If a and k are matrix functions and, accordingly, cp and f are vector-valued functions, then (1) is referred to as a system of integral equations. Integral equations of the form (1) arise in connection with many boundary value and eigenvalue problems of mathematical physics. Three types of linear integral equations are distinguished: If 2 = 0, then (1) is called an equation of the first kind; if 2a(x) i= 0 for all x E X, then (1) is termed an equation of the second kind; and finally, if a vanishes on some subset of X but 2 i= 0, then (1) is said to be of the third kind Mathematics Potential theory (Mathematics) Potential Theory Mathematik Nikol’skiĭ, S. M. Sonstige oth https://doi.org/10.1007/978-3-642-58175-5 Verlag Volltext |
| spellingShingle | Maz’ya, V. G. Analysis IV Linear and Boundary Integral Equations Mathematics Potential theory (Mathematics) Potential Theory Mathematik |
| title | Analysis IV Linear and Boundary Integral Equations |
| title_auth | Analysis IV Linear and Boundary Integral Equations |
| title_exact_search | Analysis IV Linear and Boundary Integral Equations |
| title_full | Analysis IV Linear and Boundary Integral Equations edited by V. G. Maz’ya, S. M. Nikol’skiĭ |
| title_fullStr | Analysis IV Linear and Boundary Integral Equations edited by V. G. Maz’ya, S. M. Nikol’skiĭ |
| title_full_unstemmed | Analysis IV Linear and Boundary Integral Equations edited by V. G. Maz’ya, S. M. Nikol’skiĭ |
| title_short | Analysis IV |
| title_sort | analysis iv linear and boundary integral equations |
| title_sub | Linear and Boundary Integral Equations |
| topic | Mathematics Potential theory (Mathematics) Potential Theory Mathematik |
| topic_facet | Mathematics Potential theory (Mathematics) Potential Theory Mathematik |
| url | https://doi.org/10.1007/978-3-642-58175-5 |
| work_keys_str_mv | AT mazyavg analysisivlinearandboundaryintegralequations AT nikolskiism analysisivlinearandboundaryintegralequations |