Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 873
... set i = 1 , ... , n } ( B ) { 2 | 2 = △ , \ x , ( 2 ) —x¿ ( 2 ) | < ɛ , which , since x is continuous , is open . Thus & is continuous . To see that 8-1 is continuous , i.e. , to see that & maps open sets onto open sets note first that ...
... set i = 1 , ... , n } ( B ) { 2 | 2 = △ , \ x , ( 2 ) —x¿ ( 2 ) | < ɛ , which , since x is continuous , is open . Thus & is continuous . To see that 8-1 is continuous , i.e. , to see that & maps open sets onto open sets note first that ...
Page 1151
... sets in R. We select an open set G1 in R such that F1K1CG1 , Ğ10 F2 = $ , and then choose an open set H1 such that F2OK1CH1 , H1 ~ ( F1 ~ Ğ1 ) = Þ . 1 By induction , choose open sets G and H , such that FOKCG F2OK CH 2 n n 2 ( F2H ...
... sets in R. We select an open set G1 in R such that F1K1CG1 , Ğ10 F2 = $ , and then choose an open set H1 such that F2OK1CH1 , H1 ~ ( F1 ~ Ğ1 ) = Þ . 1 By induction , choose open sets G and H , such that FOKCG F2OK CH 2 n n 2 ( F2H ...
Page 1660
... open set , " " closed set , " etc. , in this slightly modified sense . Since we deal only with multiply periodic functions throughout , all our functions will be well - defined on the set C even after the indicated identifications are ...
... open set , " " closed set , " etc. , in this slightly modified sense . Since we deal only with multiply periodic functions throughout , all our functions will be well - defined on the set C even after the indicated identifications are ...
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