Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 5
Page 1116
... C. Let y1 , . be non - overlapping differentiable arcs having a limiting direction at infinity and suppose that no ... C2 . If we let Ap1 = y / 2p ,, then 4 is plainly self adjoint and A belongs to the class C ,, where r ( 1 - p / 2 ) = p , ...
... C. Let y1 , . be non - overlapping differentiable arcs having a limiting direction at infinity and suppose that no ... C2 . If we let Ap1 = y / 2p ,, then 4 is plainly self adjoint and A belongs to the class C ,, where r ( 1 - p / 2 ) = p , ...
Page 1154
... c , ( R ( 2 ) , Σ ( 2 ) , 2 ( 2 ) ) = c ( R , Σ , λ ) × ( R , E , λ ) ... c2 ( 2 ) ( E ) for some constant c independent of E. This shows that 2 ( 2 ) ... ( BA ) , Α , Β Ε Σ . Now fix B in Σ with 0 < λ ( B ) < ∞ , and consider the measure on Σ ...
... c , ( R ( 2 ) , Σ ( 2 ) , 2 ( 2 ) ) = c ( R , Σ , λ ) × ( R , E , λ ) ... c2 ( 2 ) ( E ) for some constant c independent of E. This shows that 2 ( 2 ) ... ( BA ) , Α , Β Ε Σ . Now fix B in Σ with 0 < λ ( B ) < ∞ , and consider the measure on Σ ...
Page 1308
... C2 ( f ) = 0 , and such that ƒ vanishes in a neighborhood of b . Similarly ... BA , ( f ) = 0 , a2 + 82 0 , where A1 and A2 are real boundary values which ... C , and D¡ , pectively . i = 1 , 2 , are real boundary values at a and b res ...
... C2 ( f ) = 0 , and such that ƒ vanishes in a neighborhood of b . Similarly ... BA , ( f ) = 0 , a2 + 82 0 , where A1 and A2 are real boundary values which ... C , and D¡ , pectively . i = 1 , 2 , are real boundary values at a and b res ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
45 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero