Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1378
... Theorem 23 is unique , and 1 , ... , k ; P1 = 0 , if i > k or j > k . Pii Pij = Pij , i , j = PROOF . Suppose that σ1 , ... , σ is a determining set for T. Then it is evident from Theorem 23 that if we define { p1 ; } , i , j = 1 ...
... Theorem 23 is unique , and 1 , ... , k ; P1 = 0 , if i > k or j > k . Pii Pij = Pij , i , j = PROOF . Suppose that σ1 , ... , σ is a determining set for T. Then it is evident from Theorem 23 that if we define { p1 ; } , i , j = 1 ...
Page 1379
... THEOREM . Let τ , T , A , σ1 , ... , on , etc. , be as in Theorem 18 . Then if , for j > k , the functions 05 ( 2 ) of Theorem 18 ( or , the functions 05 ( 2 ) of Theorem 18 ) may be extended to analytic functions defined on the whole ...
... THEOREM . Let τ , T , A , σ1 , ... , on , etc. , be as in Theorem 18 . Then if , for j > k , the functions 05 ( 2 ) of Theorem 18 ( or , the functions 05 ( 2 ) of Theorem 18 ) may be extended to analytic functions defined on the whole ...
Page 1904
... theorems , IV.15 Alexandroff theorem on conver- gence of measures , ( 316 ) IV.9.15 Arzelà theorem on continuous limits , IV.6.11 ( 268 ) Banach theorem for operators into space of measurable functions , IV.11.2–3 ( 332–333 ) Egoroff ...
... theorems , IV.15 Alexandroff theorem on conver- gence of measures , ( 316 ) IV.9.15 Arzelà theorem on continuous limits , IV.6.11 ( 268 ) Banach theorem for operators into space of measurable functions , IV.11.2–3 ( 332–333 ) Egoroff ...
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