Matches in SemOpenAlex for { <https://semopenalex.org/work/W3099487369> ?p ?o ?g. }
Showing items 1 to 52 of
52
with 100 items per page.
- W3099487369 endingPage "238" @default.
- W3099487369 startingPage "219" @default.
- W3099487369 abstract "Abstract This paper deals with the equation $$-varDelta u+mu u=f$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mo>-</mml:mo> <mml:mi>Δ</mml:mi> <mml:mi>u</mml:mi> <mml:mo>+</mml:mo> <mml:mi>μ</mml:mi> <mml:mi>u</mml:mi> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> </mml:mrow> </mml:math> on high-dimensional spaces $${mathbb {R}}^m$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>m</mml:mi> </mml:msup> </mml:math> where $$mu $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>μ</mml:mi> </mml:math> is a positive constant. If the right-hand side f is a rapidly converging series of separable functions, the solution u can be represented in the same way. These constructions are based on approximations of the function 1/ r by sums of exponential functions. The aim of this paper is to prove results of similar kind for more general right-hand sides $$f(x)=F(Tx)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> <mml:mo>=</mml:mo> <mml:mi>F</mml:mi> <mml:mo>(</mml:mo> <mml:mi>T</mml:mi> <mml:mi>x</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> that are composed of a separable function on a space of a dimension n greater than m and a linear mapping given by a matrix T of full rank. These results are based on the observation that in the high-dimensional case, for $$omega $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>ω</mml:mi> </mml:math> in most of the $${mathbb {R}}^n$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:math> , the euclidian norm of the vector $$T^tomega $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:msup> <mml:mi>T</mml:mi> <mml:mi>t</mml:mi> </mml:msup> <mml:mi>ω</mml:mi> </mml:mrow> </mml:math> in the lower dimensional space $${mathbb {R}}^m$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>m</mml:mi> </mml:msup> </mml:math> behaves like the euclidian norm of $$omega $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>ω</mml:mi> </mml:math> ." @default.
- W3099487369 created "2020-11-23" @default.
- W3099487369 creator A5029894689 @default.
- W3099487369 date "2020-07-31" @default.
- W3099487369 modified "2023-10-01" @default.
- W3099487369 title "On the expansion of solutions of Laplace-like equations into traces of separable higher dimensional functions" @default.
- W3099487369 cites W2009253094 @default.
- W3099487369 cites W2053693274 @default.
- W3099487369 cites W2061170466 @default.
- W3099487369 cites W2073656615 @default.
- W3099487369 cites W3106537034 @default.
- W3099487369 cites W4239250529 @default.
- W3099487369 cites W4288938614 @default.
- W3099487369 doi "https://doi.org/10.1007/s00211-020-01138-8" @default.
- W3099487369 hasPublicationYear "2020" @default.
- W3099487369 type Work @default.
- W3099487369 sameAs 3099487369 @default.
- W3099487369 citedByCount "2" @default.
- W3099487369 countsByYear W30994873692022 @default.
- W3099487369 countsByYear W30994873692023 @default.
- W3099487369 crossrefType "journal-article" @default.
- W3099487369 hasAuthorship W3099487369A5029894689 @default.
- W3099487369 hasBestOaLocation W30994873691 @default.
- W3099487369 hasConcept C11413529 @default.
- W3099487369 hasConcept C154945302 @default.
- W3099487369 hasConcept C41008148 @default.
- W3099487369 hasConceptScore W3099487369C11413529 @default.
- W3099487369 hasConceptScore W3099487369C154945302 @default.
- W3099487369 hasConceptScore W3099487369C41008148 @default.
- W3099487369 hasFunder F4320324094 @default.
- W3099487369 hasIssue "1" @default.
- W3099487369 hasLocation W30994873691 @default.
- W3099487369 hasLocation W30994873692 @default.
- W3099487369 hasOpenAccess W3099487369 @default.
- W3099487369 hasPrimaryLocation W30994873691 @default.
- W3099487369 hasRelatedWork W2051487156 @default.
- W3099487369 hasRelatedWork W2052122378 @default.
- W3099487369 hasRelatedWork W2053286651 @default.
- W3099487369 hasRelatedWork W2073681303 @default.
- W3099487369 hasRelatedWork W2317200988 @default.
- W3099487369 hasRelatedWork W2544423928 @default.
- W3099487369 hasRelatedWork W2947381795 @default.
- W3099487369 hasRelatedWork W2181413294 @default.
- W3099487369 hasRelatedWork W2181743346 @default.
- W3099487369 hasRelatedWork W2187401768 @default.
- W3099487369 hasVolume "146" @default.
- W3099487369 isParatext "false" @default.
- W3099487369 isRetracted "false" @default.
- W3099487369 magId "3099487369" @default.
- W3099487369 workType "article" @default.