Linear Operators: Spectral theory |
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Page 1167
... ( s ) \ ' μ ( ds ) = For each such function g , put g ( a ) ( s ) = g ( s ) to ... ba¬ ́x − 1 [ f ( a ( b ) ) | ri / r + bi − 9 , −1 | f ( a ( b ) ) | P1 ... S da ] * , and is valid whenever k≥1 . Using this and ( XI.11.14 NOTES AND ...
... ( s ) \ ' μ ( ds ) = For each such function g , put g ( a ) ( s ) = g ( s ) to ... ba¬ ́x − 1 [ f ( a ( b ) ) | ri / r + bi − 9 , −1 | f ( a ( b ) ) | P1 ... S da ] * , and is valid whenever k≥1 . Using this and ( XI.11.14 NOTES AND ...
Page 1885
... ba ( S , Σ ) ( 240 ) f ( T ) ( 557 ) , ( 568 ) , ( 601 ) , ( 1196 ) ba ( S , Σ , x ) ( 160 ) f.g ( 633 ) , ( 951 ) bs ( 240 ) ƒ Š ( 951 ) bv ( 239 ) F ( f . g ) ( 1287 ) bvo ( 239 ) F ( + ) ( 1287 ) ( B ( 895 ) || F || ( k ) ( 1663 ) B ...
... ba ( S , Σ ) ( 240 ) f ( T ) ( 557 ) , ( 568 ) , ( 601 ) , ( 1196 ) ba ( S , Σ , x ) ( 160 ) f.g ( 633 ) , ( 951 ) bs ( 240 ) ƒ Š ( 951 ) bv ( 239 ) F ( f . g ) ( 1287 ) bvo ( 239 ) F ( + ) ( 1287 ) ( B ( 895 ) || F || ( k ) ( 1663 ) B ...
Page 1893
... S. , 233 Lebesgue , H. , 80 , 124 , 132 , 143 , 151 , 218 , 232 , 234 , 390 Lefschetz , S. , 47 , 467 Legendre , A. M. , 1512 Leja , F. , 79 Lengyel , B. A. , 927 , 928 , 929 Leray , J. , 84 , 470 , 609 Levi , B. , 373 Levinson , N ...
... S. , 233 Lebesgue , H. , 80 , 124 , 132 , 143 , 151 , 218 , 232 , 234 , 390 Lefschetz , S. , 47 , 467 Legendre , A. M. , 1512 Leja , F. , 79 Lengyel , B. A. , 927 , 928 , 929 Leray , J. , 84 , 470 , 609 Levi , B. , 373 Levinson , N ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Copyright | |
59 other sections not shown
Common terms and phrases
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 deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero