Linear Operators, Part 2 |
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Page 1380
... similar . Q.E.D. i ij , 30 COROLLARY . Let τ , T , A , σ¿ , O ‡ ¡ , etc. , be as in Theorem 18 . Then an isolated point λ e Ao ( T ) is an isolated singularity of Ot , ( or , equivalently , of 0¡¡ ) . Moreover , p¡¡ ( { 2 } ) is the ...
... similar . Q.E.D. i ij , 30 COROLLARY . Let τ , T , A , σ¿ , O ‡ ¡ , etc. , be as in Theorem 18 . Then an isolated point λ e Ao ( T ) is an isolated singularity of Ot , ( or , equivalently , of 0¡¡ ) . Moreover , p¡¡ ( { 2 } ) is the ...
Page 1385
... similar computation and deriving an exactly similar result in case ( ii ) . In cases ( iii ) and ( iv ) the function ( k√ −λ − 1 ) e√ − λt + ( k√ −λ + 1 ) e - √λt satisfies f ( 0 ) + kf ' ( 0 XIII.5.31 1385 SPECTRAL THEORY ...
... similar computation and deriving an exactly similar result in case ( ii ) . In cases ( iii ) and ( iv ) the function ( k√ −λ − 1 ) e√ − λt + ( k√ −λ + 1 ) e - √λt satisfies f ( 0 ) + kf ' ( 0 XIII.5.31 1385 SPECTRAL THEORY ...
Page 1592
... similar to that which has been given by Picone [ 1 ] . Corollary 37 goes back to Kneser [ 1 ] . The study of the connection between the essential spectrum and the oscillatory behavior of the solutions was initiated by Hartman [ 8 ] and ...
... similar to that which has been given by Picone [ 1 ] . Corollary 37 goes back to Kneser [ 1 ] . The study of the connection between the essential spectrum and the oscillatory behavior of the solutions was initiated by Hartman [ 8 ] and ...
Contents
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