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On the ground state of some fractional Laplacian‐like operators
Author(s) -
Sobolev Alexander V.
Publication year - 2014
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdu036
Subject(s) - mathematics , degenerate energy levels , elliptic operator , laplace operator , eigenvalues and eigenvectors , operator (biology) , p laplacian , generalization , semigroup , homogeneous , pure mathematics , domain (mathematical analysis) , hermitian matrix , measure (data warehouse) , mathematical analysis , combinatorics , boundary value problem , physics , quantum mechanics , database , computer science , transcription factor , gene , biochemistry , chemistry , repressor
On a domain of finite measure, we study the elliptic operator with a homogeneous Hermitian symbol of degree γ ∈ ( 0 , 2 ) , which is a generalization of the standard fractional Laplacian. We prove that the semigroup of this operator is positivity improving, and as a consequence, its eigenvalue with the smallest real part is real and non‐degenerate.