Linear Operators: Spectral theory |
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Page 1144
... resolvent of T 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 ...
... resolvent of T 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 ...
Page 1187
... resolvent set p ( T ) of an operator T is defined to be the set of all complex numbers such that ( 1 - T ) -1 exists as an everywhere defined bounded operator . For 2 in p ( T ) the symbol R ( λ ; T ) will be used for the resolvent ...
... resolvent set p ( T ) of an operator T is defined to be the set of all complex numbers such that ( 1 - T ) -1 exists as an everywhere defined bounded operator . For 2 in p ( T ) the symbol R ( λ ; T ) will be used for the resolvent ...
Page 1422
... resolvent set of S. Since , by Lemma XII.1.3 , the resolvent set is open , μ 。 is not in the resolvent set . Suppose < ∞ , and let μ , be a sequence of real numbers approaching μ from below . By [ †† ] , | R ( −μ „ i ; S ) \ ≤ μñ1 ...
... resolvent set of S. Since , by Lemma XII.1.3 , the resolvent set is open , μ 。 is not in the resolvent set . Suppose < ∞ , and let μ , be a sequence of real numbers approaching μ from below . By [ †† ] , | R ( −μ „ i ; S ) \ ≤ μñ1 ...
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