Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1279
... interval of the real axis . The interval I can be open , half - open , or closed . The interval [ a , co ) is considered to be half - open ; the interval ( ∞ , ∞ ) to be open . Thus a closed interval is a compact set . An end point t ...
... interval of the real axis . The interval I can be open , half - open , or closed . The interval [ a , co ) is considered to be half - open ; the interval ( ∞ , ∞ ) to be open . Thus a closed interval is a compact set . An end point t ...
Page 1539
... interval [ 0 , ∞ ) . Prove that a complex number 2 belongs to the essential spectrum of 7 if and only if there exists a sequence { f } of functions in D ( To ( T ) ) such that │f2 = 1 , f2 vanishes in the interval [ 0 , n ] , and as n ...
... interval [ 0 , ∞ ) . Prove that a complex number 2 belongs to the essential spectrum of 7 if and only if there exists a sequence { f } of functions in D ( To ( T ) ) such that │f2 = 1 , f2 vanishes in the interval [ 0 , n ] , and as n ...
Page 1599
... interval [ 0 , ∞ ) . Then on the positive real axis every interval of length K contains a point of the essential spectrum of 7 ( Glazman [ 4 ] , Exercise 9.A 6 ) . ( 32 ) On the interval [ 0 , ∞ ) , if q ( t ) tends monotonically to ...
... interval [ 0 , ∞ ) . Then on the positive real axis every interval of length K contains a point of the essential spectrum of 7 ( Glazman [ 4 ] , Exercise 9.A 6 ) . ( 32 ) On the interval [ 0 , ∞ ) , if q ( t ) tends monotonically to ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero