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Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen
Open accessAbstract
Es sei K (s, t) eine Funktion der reellen Veränderlichen s, t; f(s) sei eine gegebene Funktion von s und ϕ (s) werde als die zu bestimmende Funktion von s angesehen; jede der Veränderlichen s, t möge sieh in dem Intervalle a bis b bewegen: dann heiße $$ f(s) = \int_a^b K (s,t){\rm{\phi }}(t)dt $$ eine Integralgleichung erster Art und $$ f(s) = {\rm{\phi }}(s) - \lambda \int_a^b K (s,t){\rm{\phi }}(t)dt $$ eine Integralgleichung zweiter Art; dabei bedeutet λ einen Parameter. Die Funktion K(s, t) heiße der Kern der Integralgleichungen.
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Rayleigh, L., & Nachtrieb, N. H. (1957) · Physics Today · doi:10.1063/1.3060230 · Cited by 3,464
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Nirenberg, L. (1953) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160060303 · Cited by 447
Zur Theorie der linearen und nichtlinearen Integralgleichungen
Schmidt, E. (1989) · Teubner-Archiv zur Mathematik · doi:10.1007/978-3-322-84410-1_3 · Cited by 379
Stip, E., Caron, J., Renaud, S., Pampoulova, T., & Lecomte, Y. (2003) · Comprehensive Psychiatry · doi:10.1016/s0010-440x(03)00086-5 · Cited by 214
Metadata
- Authors
- Hilbert, D.
- Venue
- Teubner-Archiv zur Mathematik
- Publisher
- Vieweg+Teubner Verlag
- Published
- 1989
- Pages
- 8-171
- ISSN
- 0233-0962 (ISSN-L)
- OpenAlex
- W2064976291
- Cited by
- 450
- References
- 1
- FWCI
- 11.39
- Type
- book chapter
- Language
- de
- Open access
- green
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