Linear Operators: Spectral theory |
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Page 1310
... solution y of ( T - λ ) y 0 square - integrable at b and satisfying all boundary conditions at b , and at least one solution q of ( 7-2 ) = 0 square - integrable at a and satisfying all the boundary conditions at a . Suppose there were ...
... solution y of ( T - λ ) y 0 square - integrable at b and satisfying all boundary conditions at b , and at least one solution q of ( 7-2 ) = 0 square - integrable at a and satisfying all the boundary conditions at a . Suppose there were ...
Page 1521
... solution of the order of t - 1 - i as t → ∞ and another which behaves like ti as too . The solution at λ = 1 - i is exactly similar . Thus , by Theorem XII.4.19 , L1 - λ has precisely one solution belonging to L2 ( 2 , ∞ ) for each ...
... solution of the order of t - 1 - i as t → ∞ and another which behaves like ti as too . The solution at λ = 1 - i is exactly similar . Thus , by Theorem XII.4.19 , L1 - λ has precisely one solution belonging to L2 ( 2 , ∞ ) for each ...
Page 1556
... solution of the above equation ? G14 Use the result of the preceding exercise to show that if the operator has two boundary values at infinity , then lim 017 N ( t ) t2 - ∞ , where N ( t ) is the number of zeros of a solution of the ...
... solution of the above equation ? G14 Use the result of the preceding exercise to show that if the operator has two boundary values at infinity , then lim 017 N ( t ) t2 - ∞ , where N ( t ) is the number of zeros of a solution of the ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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