Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1036
... converges absolutely provided that λ λ for any k . In view of the fact that → 0 it follows from the estimate in ( * ) that the series ∞ k - 1 log ( etwa ( 1-4 ) ) λ converges uniformly and absolutely for each compact set of numbers 2 ...
... converges absolutely provided that λ λ for any k . In view of the fact that → 0 it follows from the estimate in ( * ) that the series ∞ k - 1 log ( etwa ( 1-4 ) ) λ converges uniformly and absolutely for each compact set of numbers 2 ...
Page 1436
... converges , then { f } converges . Let { g } be a bounded sequence of elements of D ( T ) such that { Tg , } converges . Find a subsequence { g } = { h } such that x * ( h ) converges for each j , 1 ≤ j ≤k . Then h ̧ = h ̧ — Σ_1x ...
... converges , then { f } converges . Let { g } be a bounded sequence of elements of D ( T ) such that { Tg , } converges . Find a subsequence { g } = { h } such that x * ( h ) converges for each j , 1 ≤ j ≤k . Then h ̧ = h ̧ — Σ_1x ...
Page 1664
... converges unconditionally to F. PROOF . It follows from the Definition 37 of the topology in D ( C ) that it suffices to show that -n ΣΕ L ( 2 ) Ic L eiLq ( x ) dx converges unconditionally to F ( q ) for each q in C ( C ) . For any set ...
... converges unconditionally to F. PROOF . It follows from the Definition 37 of the topology in D ( C ) that it suffices to show that -n ΣΕ L ( 2 ) Ic L eiLq ( x ) dx converges unconditionally to F ( q ) for each q in C ( C ) . For any set ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula 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 linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero