Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1599
... essential spectrum of 7 is void ( Berkowitz [ 1 ] ) . Other conditions which allow the approximate determination of the essential spectrum are the following : ( 31 ) Let K = lim sup q ( t ) - lim inf q ( t ) in the interval [ 0 ...
... essential spectrum of 7 is void ( Berkowitz [ 1 ] ) . Other conditions which allow the approximate determination of the essential spectrum are the following : ( 31 ) Let K = lim sup q ( t ) - lim inf q ( t ) in the interval [ 0 ...
Page 1600
... essential spectrum of but whose end points belong to the essential spectrum of t . If then f ' " ' \ q ' ' ( s ) \ ds = O ( t ) , | λ — μ | = 0 ( Hartman and Putnam [ 2 ] ) . then ( ) ( 37 ) Similarly , if q is three times ...
... essential spectrum of but whose end points belong to the essential spectrum of t . If then f ' " ' \ q ' ' ( s ) \ ds = O ( t ) , | λ — μ | = 0 ( Hartman and Putnam [ 2 ] ) . then ( ) ( 37 ) Similarly , if q is three times ...
Page 1613
... essential spectrum is to be defined as in Section 6 , and is a closed subset of the complex plane which coincides with the essential spectrum of the formal adjoint operator in the conjugate space . The essential spectrum of a formal ...
... essential spectrum is to be defined as in Section 6 , and is a closed subset of the complex plane which coincides with the essential spectrum of the formal adjoint operator in the conjugate space . The essential spectrum of a formal ...
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