Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1900
... definition , IV.2.25 ( 242 ) remarks concerning , ( 386-387 ) study of , IV.7 Almost uniform ( or μ - uniform conver- gence ) definition , III . 6.1 ( 145 ) . ( See also Convergence of func- tions ) Analytic continuation , ( 230 ) ...
... definition , IV.2.25 ( 242 ) remarks concerning , ( 386-387 ) study of , IV.7 Almost uniform ( or μ - uniform conver- gence ) definition , III . 6.1 ( 145 ) . ( See also Convergence of func- tions ) Analytic continuation , ( 230 ) ...
Page 1907
... definition , VII.1.2 ( 556 ) , VII.11 ( 606 ) , X.3.1 ( 902 ) Eigenvector , definition , VII.1.2 ( 556 ) , X.3.1 ( 903 ) Embedding , natural , of a B - space into` its second conjugate , II.3.18 ( 66 ) End point of an interval , III ...
... definition , VII.1.2 ( 556 ) , VII.11 ( 606 ) , X.3.1 ( 902 ) Eigenvector , definition , VII.1.2 ( 556 ) , X.3.1 ( 903 ) Embedding , natural , of a B - space into` its second conjugate , II.3.18 ( 66 ) End point of an interval , III ...
Page 1921
... definition , VII.7 ( 458 ) Strong operator topology , definition , VI.1.2 ( 475 ) properties , VI.9.1–5 ( 511 ) , VI.9.11– 12 ( 512-513 ) Strong topology , in a normed space , II.3.1 ( 59 ) , ( 419 ) Structure space of a B - algebra ...
... definition , VII.7 ( 458 ) Strong operator topology , definition , VI.1.2 ( 475 ) properties , VI.9.1–5 ( 511 ) , VI.9.11– 12 ( 512-513 ) Strong topology , in a normed space , II.3.1 ( 59 ) , ( 419 ) Structure space of a B - algebra ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero