SOBOLEV SPACES ON LOCALLY COMPACT ABELIAN GROUPS AND THE BOSONIC STRING EQUATION
2014 ◽
Vol 98
(1)
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pp. 39-53
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Keyword(s):
AbstractMotivated by a class of nonlinear nonlocal equations of interest for string theory, we introduce Sobolev spaces on arbitrary locally compact abelian groups and we examine some of their properties. Specifically, we focus on analogs of the Sobolev embedding and Rellich–Kondrachov compactness theorems. As an application, we prove the existence of continuous solutions to a generalized bosonic string equation posed on an arbitrary compact abelian group, and we also remark that our approach allows us to solve very general linear equations in a $p$-adic context.
2020 ◽
Vol 18
(04)
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pp. 2050019
1994 ◽
Vol 126
(1)
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pp. 1-6
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1966 ◽
Vol 62
(3)
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pp. 399-420
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Keyword(s):
2021 ◽
Vol 10
(4)
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pp. 2033-2044
1946 ◽
Vol 52
(10)
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pp. 940-945
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Keyword(s):
Keyword(s):
2011 ◽
Vol 48
(5)
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pp. 899-912
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