Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1057
... exists . Thus , to complete the proof of the present lemma , it suffices to show that ( 3 ) O ( u ) = P S Ω ( Μ ) En yn eivu dy -- lim S Ω ( ψ ) eiyu dy ESVSR yn R - ∞ exists for each u . By Lemma 2 , the integral ( tu ) exists if 0 ( u ) ...
... exists . Thus , to complete the proof of the present lemma , it suffices to show that ( 3 ) O ( u ) = P S Ω ( Μ ) En yn eivu dy -- lim S Ω ( ψ ) eiyu dy ESVSR yn R - ∞ exists for each u . By Lemma 2 , the integral ( tu ) exists if 0 ( u ) ...
Page 1261
... exists a unique closed linear extension T such that if T1 is any closed linear extension of T then TCT1 . T is called the closure of T. ( a ) There exists a densely defined operator with no closed linear extension . ( b ) An operator T ...
... exists a unique closed linear extension T such that if T1 is any closed linear extension of T then TCT1 . T is called the closure of T. ( a ) There exists a densely defined operator with no closed linear extension . ( b ) An operator T ...
Page 1733
... exists a neighborhood V1 of Zo such that f | V1I is in H ( ) ( V1I ) , there also exists a neighborhood V2 of such that f | V2I is in H ( * + 1 ) ( V2I ) . 1 2 Proof that Lemma 20 implies Lemma 19. By the hypothesis of Lemma 19 , we ...
... exists a neighborhood V1 of Zo such that f | V1I is in H ( ) ( V1I ) , there also exists a neighborhood V2 of such that f | V2I is in H ( * + 1 ) ( V2I ) . 1 2 Proof that Lemma 20 implies Lemma 19. By the hypothesis of Lemma 19 , we ...
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