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Page 1210
... measure space . Let E be the resolution of the identity for T. We assume that there exists an increasing sequence { S } covering S , each element of which has finite . measure , and that for bounded sets e the range of E ( e ) contains ...
... measure space . Let E be the resolution of the identity for T. We assume that there exists an increasing sequence { S } covering S , each element of which has finite . measure , and that for bounded sets e the range of E ( e ) contains ...
Page 1900
... space of , additional properties , IV.15 ( 379 ) definition , IV.2.25 ( 242 ) remarks concerning , ( 386–387 ) study ... measure space , IV.9.6 ( 308 ) Automorphisms , in groups , ( 35 ) B B - algebra . ( See Algebra ) B * -algebras , IX ...
... space of , additional properties , IV.15 ( 379 ) definition , IV.2.25 ( 242 ) remarks concerning , ( 386–387 ) study ... measure space , IV.9.6 ( 308 ) Automorphisms , in groups , ( 35 ) B B - algebra . ( See Algebra ) B * -algebras , IX ...
Page 1913
... space , VIII.7.1-3 ( 687-689 ) in L1 , VIII.7.4 ( 689 ) in L , VIII.7.10 ... Measure . ( See also Set function ) Borel or Borel - Lebesgue , ( 139 ) ... Measure space , decomposition of . ( See also Decomposition ) definition , III.4.3 ...
... space , VIII.7.1-3 ( 687-689 ) in L1 , VIII.7.4 ( 689 ) in L , VIII.7.10 ... Measure . ( See also Set function ) Borel or Borel - Lebesgue , ( 139 ) ... Measure space , decomposition of . ( See also Decomposition ) definition , III.4.3 ...
Contents
BAlgebras | 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 complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero