Interpolation theorems for self-adjoint operators
نویسندگان
چکیده
منابع مشابه
Interpolation Theorems for Self-adjoint Operators
We prove a complex and a real interpolation theorems on Besov spaces and Triebel-Lizorkin spaces associated with a selfadjoint operator L, without assuming the gradient estimate for its spectral kernel. The result applies to the cases where L is a uniformly elliptic operator or a Schrödinger operator with electromagnetic potential.
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Lemma 1.2 (An Eigenvector Basis Diagonalizes T ). Let V be an n-dimensional vector space over a field F, and let T : V → V be a linear transformation. Suppose V has an ordered basis β := (v1, . . . , vn). Then vi is an eigenvector of T with eigenvalue λi ∈ F, for all i ∈ {1, . . . , n}, if and only if the matrix [T ]ββ is diagonal with [T ] β β = diag(λ1, . . . , λn). Lemma 1.3. Let V be a fini...
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ژورنال
عنوان ژورنال: Analysis in Theory and Applications
سال: 2009
ISSN: 1672-4070,1573-8175
DOI: 10.1007/s10496-009-0079-y