Linear Operators, Part 2 |
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Page 1144
... satisfies the inequality | R ( 2 ; T ) | = O ( | 2 | -N ) as 20 along any of the arcs 7. Then the subspace sp ( T ) contains the subspace TNS . Similarly , by arguing as in the proofs of Corollary 6.30 and Corollary 6.31 , we obtain the ...
... satisfies the inequality | R ( 2 ; T ) | = O ( | 2 | -N ) as 20 along any of the arcs 7. Then the subspace sp ( T ) contains the subspace TNS . Similarly , by arguing as in the proofs of Corollary 6.30 and Corollary 6.31 , we obtain the ...
Page 1385
... satisfies the boundary condition f ( 0 ) + kf ' ( 0 ) if and only if 1 - k - λ = 0 ; i.e. , if and only if k is positive and λ = -1 / k2 . Thus , only in case ( iv ) does T have a non - void point spectrum , which consists of the single ...
... satisfies the boundary condition f ( 0 ) + kf ' ( 0 ) if and only if 1 - k - λ = 0 ; i.e. , if and only if k is positive and λ = -1 / k2 . Thus , only in case ( iv ) does T have a non - void point spectrum , which consists of the single ...
Page 1602
... satisfies f ' " ' \ f ( s ) | 3 ds = O ( t * ) for some k > 0. Then the point λ belongs to the essential spectrum of T ( Wintner [ 17 ] ) . ( 49 ) Suppose that the function q is bounded below , and that for some constant k > 0 every ...
... satisfies f ' " ' \ f ( s ) | 3 ds = O ( t * ) for some k > 0. Then the point λ belongs to the essential spectrum of T ( Wintner [ 17 ] ) . ( 49 ) Suppose that the function q is bounded below , and that for some constant k > 0 every ...
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BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant 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(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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero