Linear Operators: Spectral theory |
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Page 1099
... arbitrarily closely by non - singular matrices , it is sufficient to consider the case in which T is non - singular . Then A = ( TT * ) 1/2 is also non - singular and if U = A - 1T , UU * = A - 1 A2A - 1 = 1 , then U is unitary ...
... arbitrarily closely by non - singular matrices , it is sufficient to consider the case in which T is non - singular . Then A = ( TT * ) 1/2 is also non - singular and if U = A - 1T , UU * = A - 1 A2A - 1 = 1 , then U is unitary ...
Page 1184
X , Ye A 1x - yle - XEA These B - spaces have been studied extensively in connection with the theory of singular integrals . Singular integrals of Hilbert - CalderónZygmund type may be shown under suitable hypotheses to map functions ...
X , Ye A 1x - yle - XEA These B - spaces have been studied extensively in connection with the theory of singular integrals . Singular integrals of Hilbert - CalderónZygmund type may be shown under suitable hypotheses to map functions ...
Page 1919
o - finite , III.5.7 ( 136 ) singular , III.4.12 ( 131 ) spaces of , as conjugate spaces , IV.5.1 ( 258 ) , IV.5.3 ( 259 ) , IV.6.2–3 ( 262–264 ) , IV.8.16 ( 296 ) definitions , ( 160–162 ) , IV.2.15-17 ( 240 ) , IV.6.1 ( 261 ) remarks ...
o - finite , III.5.7 ( 136 ) singular , III.4.12 ( 131 ) spaces of , as conjugate spaces , IV.5.1 ( 258 ) , IV.5.3 ( 259 ) , IV.6.2–3 ( 262–264 ) , IV.8.16 ( 296 ) definitions , ( 160–162 ) , IV.2.15-17 ( 240 ) , IV.6.1 ( 261 ) remarks ...
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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