Linear Operators: Spectral theory |
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Page 1379
ܕ be the ies ( 0 ) = 1 { Ô is } is the matrix measure of Theorem 23 , the values Pij ( e ) are uniquely determined for each e CN . Since 1 is the union of a sequence of neighborhoods of the same type as N , the uniqueness of { u } ...
ܕ be the ies ( 0 ) = 1 { Ô is } is the matrix measure of Theorem 23 , the values Pij ( e ) are uniquely determined for each e CN . Since 1 is the union of a sequence of neighborhoods of the same type as N , the uniqueness of { u } ...
Page 1904
IV.15 Alexandroff theorem gence of measures , IV.9.15 ( 316 ) Arzela theorem continuous limits , IV.6.11 ( 268 ) Banach theorem for operators into Egoroff theorem on a.e. and u - uniform convergence , III.6.12 ( 149 ) Fatou theorem on ...
IV.15 Alexandroff theorem gence of measures , IV.9.15 ( 316 ) Arzela theorem continuous limits , IV.6.11 ( 268 ) Banach theorem for operators into Egoroff theorem on a.e. and u - uniform convergence , III.6.12 ( 149 ) Fatou theorem on ...
Page 1923
( 150 ) , II1.9.45 , IV.10.9 ( 325 ) covering theorem , II1.12.2 ( 212 ) W definition , VI.4.1 ( 482 ) in Li , V1.8.1 ( 498 ) , VI.8.10–14 ( 507510 ) in Loo , VI.9.57 ( 519 ) remarks on , ( 539 ) , ( 541 ) representation of ...
( 150 ) , II1.9.45 , IV.10.9 ( 325 ) covering theorem , II1.12.2 ( 212 ) W definition , VI.4.1 ( 482 ) in Li , V1.8.1 ( 498 ) , VI.8.10–14 ( 507510 ) in Loo , VI.9.57 ( 519 ) remarks on , ( 539 ) , ( 541 ) representation of ...
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Contents
8 | 876 |
859 | 885 |
extensive presentation of applications of the spectral theorem | 911 |
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additive adjoint adjoint operator algebra analytic assume basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero