Linear Operators: Spectral theory |
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Page 1255
... s ) f ( t ) g ( s ) ; since this sum has only finitely many non - zero terms it is well defined . Then ( f , g ) is ... CA. Con- sequently , we can define a mapping U ( t ) : B → B by letting U ( t ) x = V ( t ) f + o , if x = = f + A is in ...
... s ) f ( t ) g ( s ) ; since this sum has only finitely many non - zero terms it is well defined . Then ( f , g ) is ... CA. Con- sequently , we can define a mapping U ( t ) : B → B by letting U ( t ) x = V ( t ) f + o , if x = = f + A is in ...
Page 1676
... Ca ( C ) . Since S1 = √13 for each index J , we have also ( o ) ≤ follows from Definition 34 that part of ( i ) is ... ( S ̧F ) ( 9 ) = −4 - 1 √ , F ( x ) { [ 2,1 * ^ q ( s , x2 , . . . , x ' , ) ds ) dx - x1 = − 4 - 1 S c { [ " _ ̧ Ƒ ...
... Ca ( C ) . Since S1 = √13 for each index J , we have also ( o ) ≤ follows from Definition 34 that part of ( i ) is ... ( S ̧F ) ( 9 ) = −4 - 1 √ , F ( x ) { [ 2,1 * ^ q ( s , x2 , . . . , x ' , ) ds ) dx - x1 = − 4 - 1 S c { [ " _ ̧ Ƒ ...
Page 1885
... ( S , Σ ) ( 240 ) Flo ( 1649 ) BV ( I ) ( 241 ) B ( X , Y ) ( 61 ) F ( S ) or F ( S , 2 , μ , X ) ( 103 ) F ( T ) ( 557 ) , ( 568 ) , ( 600 ) F ( α , B ; Y ; z ) ( 1509 ) c ( 239 ) FT ( C ) ( 1660 ) Co ( 239 ) ca ( S , Σ ) ( 240 ) glb A ( 3 ) ...
... ( S , Σ ) ( 240 ) Flo ( 1649 ) BV ( I ) ( 241 ) B ( X , Y ) ( 61 ) F ( S ) or F ( S , 2 , μ , X ) ( 103 ) F ( T ) ( 557 ) , ( 568 ) , ( 600 ) F ( α , B ; Y ; z ) ( 1509 ) c ( 239 ) FT ( C ) ( 1660 ) Co ( 239 ) ca ( S , Σ ) ( 240 ) glb A ( 3 ) ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero