Linear Operators: Spectral theory |
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Page 1064
... satisfies the inequality g , ≤IA , ƒ „ , where I ms - Ss 2 ( w ) u ( do ) . To do this , let { m } be a sequence of odd functions , each infinitely often differentiable in the neighborhood of the unit sphere , such that 2m ( tx ) = 2m ...
... satisfies the inequality g , ≤IA , ƒ „ , where I ms - Ss 2 ( w ) u ( do ) . To do this , let { m } be a sequence of odd functions , each infinitely often differentiable in the neighborhood of the unit sphere , such that 2m ( tx ) = 2m ...
Page 1144
... satisfies the inequality | R ( λ ; T ) | = O ( | λ2 | ~~ ) as → 0 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 ...
... satisfies the inequality | R ( λ ; T ) | = O ( | λ2 | ~~ ) as → 0 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 ...
Page 1602
... satisfies [ ' * ' \ f ( s ) [ 2 ds = O ( t * ) for some k > 0 . Then the point 2 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 ( s ) [ 2 ds = O ( t * ) for some k > 0 . Then the point 2 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 ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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 Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero