Matches in SemOpenAlex for { <https://semopenalex.org/work/W2092998961> ?p ?o ?g. }
Showing items 1 to 83 of
83
with 100 items per page.
- W2092998961 endingPage "167" @default.
- W2092998961 startingPage "154" @default.
- W2092998961 abstract "In this paper, a method called “differential inversion” is presented for solving a class of integral equations (Fredholm integral equations of the first kind) of convolution form. Differential inversion (DI) is presented as an alternative to Fourier transform methods. The method expresses the unknown function as a series of successive derivatives of the known function. The known-unknown functions are evaluated at the same point. This new expansion is not to be confused with a Taylor expansion, although we show that every Taylor expansion is a differential inversion expansion. Differential inversion is shown to be related to Gauss’s multipole expansion of a field at large distances from its source. The fundamental mathematical objects in this theory are generalizations of distributions, which we term “generalized distributions” or “hyperdistributions.” An important feature of our method is that convolutions form a closed algebraic field in the space of hyperdistributions. The relation of this field to Mikusiński’s field is discussed. A major result of our analysis is to give an explicit construction of the convolution inverse for any element of our field. The coefficients in the differential inversion series may be computed from the moments of the kernel. The inversion of convolution equations with exponential and Gaussian kernels is demonstrated in this paper (although the method may be applied to any kernel with finite moments). In particular, unique solutions are obtained in the space of hyperdistributions, even in those cases that cannot be represented by convergent Fourier integrals. The choices of kernels made here are relevant to a number of physical problems in signal processing, image processing, radiative transfer, and other inverse problems." @default.
- W2092998961 created "2016-06-24" @default.
- W2092998961 creator A5041790665 @default.
- W2092998961 creator A5067665076 @default.
- W2092998961 creator A5082620363 @default.
- W2092998961 creator A5088521778 @default.
- W2092998961 date "1993-02-01" @default.
- W2092998961 modified "2023-09-23" @default.
- W2092998961 title "Solution of Convolution Integral Equations by the Method of Differential Inversion" @default.
- W2092998961 cites W1980983568 @default.
- W2092998961 cites W2007287149 @default.
- W2092998961 cites W2154231179 @default.
- W2092998961 cites W2159419754 @default.
- W2092998961 cites W4205109918 @default.
- W2092998961 doi "https://doi.org/10.1137/0153010" @default.
- W2092998961 hasPublicationYear "1993" @default.
- W2092998961 type Work @default.
- W2092998961 sameAs 2092998961 @default.
- W2092998961 citedByCount "19" @default.
- W2092998961 countsByYear W20929989612016 @default.
- W2092998961 countsByYear W20929989612018 @default.
- W2092998961 countsByYear W20929989612019 @default.
- W2092998961 countsByYear W20929989612021 @default.
- W2092998961 crossrefType "journal-article" @default.
- W2092998961 hasAuthorship W2092998961A5041790665 @default.
- W2092998961 hasAuthorship W2092998961A5067665076 @default.
- W2092998961 hasAuthorship W2092998961A5082620363 @default.
- W2092998961 hasAuthorship W2092998961A5088521778 @default.
- W2092998961 hasConcept C102519508 @default.
- W2092998961 hasConcept C109007969 @default.
- W2092998961 hasConcept C119857082 @default.
- W2092998961 hasConcept C134306372 @default.
- W2092998961 hasConcept C151730666 @default.
- W2092998961 hasConcept C158946198 @default.
- W2092998961 hasConcept C186080144 @default.
- W2092998961 hasConcept C1893757 @default.
- W2092998961 hasConcept C203024314 @default.
- W2092998961 hasConcept C207864730 @default.
- W2092998961 hasConcept C33923547 @default.
- W2092998961 hasConcept C41008148 @default.
- W2092998961 hasConcept C45347329 @default.
- W2092998961 hasConcept C50644808 @default.
- W2092998961 hasConcept C76563020 @default.
- W2092998961 hasConcept C86254553 @default.
- W2092998961 hasConcept C86803240 @default.
- W2092998961 hasConceptScore W2092998961C102519508 @default.
- W2092998961 hasConceptScore W2092998961C109007969 @default.
- W2092998961 hasConceptScore W2092998961C119857082 @default.
- W2092998961 hasConceptScore W2092998961C134306372 @default.
- W2092998961 hasConceptScore W2092998961C151730666 @default.
- W2092998961 hasConceptScore W2092998961C158946198 @default.
- W2092998961 hasConceptScore W2092998961C186080144 @default.
- W2092998961 hasConceptScore W2092998961C1893757 @default.
- W2092998961 hasConceptScore W2092998961C203024314 @default.
- W2092998961 hasConceptScore W2092998961C207864730 @default.
- W2092998961 hasConceptScore W2092998961C33923547 @default.
- W2092998961 hasConceptScore W2092998961C41008148 @default.
- W2092998961 hasConceptScore W2092998961C45347329 @default.
- W2092998961 hasConceptScore W2092998961C50644808 @default.
- W2092998961 hasConceptScore W2092998961C76563020 @default.
- W2092998961 hasConceptScore W2092998961C86254553 @default.
- W2092998961 hasConceptScore W2092998961C86803240 @default.
- W2092998961 hasIssue "1" @default.
- W2092998961 hasLocation W20929989611 @default.
- W2092998961 hasOpenAccess W2092998961 @default.
- W2092998961 hasPrimaryLocation W20929989611 @default.
- W2092998961 hasRelatedWork W1822672720 @default.
- W2092998961 hasRelatedWork W1985797048 @default.
- W2092998961 hasRelatedWork W1991154990 @default.
- W2092998961 hasRelatedWork W1995492390 @default.
- W2092998961 hasRelatedWork W1999530669 @default.
- W2092998961 hasRelatedWork W2043591526 @default.
- W2092998961 hasRelatedWork W2181789249 @default.
- W2092998961 hasRelatedWork W2575524817 @default.
- W2092998961 hasRelatedWork W4300772523 @default.
- W2092998961 hasRelatedWork W978466576 @default.
- W2092998961 hasVolume "53" @default.
- W2092998961 isParatext "false" @default.
- W2092998961 isRetracted "false" @default.
- W2092998961 magId "2092998961" @default.
- W2092998961 workType "article" @default.