| ID | 62794 |
| FullText URL | |
| Author |
Yamagishi, Hiroyuki
Tokyo Metropolitan College of Industrial Technology
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| Abstract | We have the best constants of three kinds of discrete Sobolev inequalities on the complete bipartite graph with 2N vertices, that is, KN,N. We introduce a discrete Laplacian A on KN,N. A is a 2N ×2N real symmetric positive-semidefinite matrix whose eigenvector corresponding to zero eigenvalue is 1 = t(1, 1, … , 1)∈ C2N. A discrete heat kernel, a Green’s matrix and a pseudo Green’s matrix play important roles in giving the best constants.
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| Keywords | Discrete Sobolev inequality
Discrete Laplacian
Green’s matrix
Reproducing relation
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| Note | Mathematics Subject Classification. Primary 46E39; Secondary 35K08.
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| Published Date | 2022-01
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| Publication Title |
Mathematical Journal of Okayama University
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| Volume | volume64
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| Issue | issue1
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| Publisher | Department of Mathematics, Faculty of Science, Okayama University
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| Start Page | 31
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| End Page | 45
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| ISSN | 0030-1566
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| NCID | AA00723502
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| Content Type |
Journal Article
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| language |
English
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| Copyright Holders | Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
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| File Version | publisher
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| Refereed |
True
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| Submission Path | mjou/vol64/iss1/3
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