Linear Operators: Spectral theory |
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Page 1505
... equation L'f " 0 satisfied by f " = f [ p ( z ) ] has rational coefficients also . The operator L " has a regular sin- gularity at So with exponents le1 , le . = 0 By passing from the equation Lf = 0 to the equation L ' ' ' f ...
... equation L'f " 0 satisfied by f " = f [ p ( z ) ] has rational coefficients also . The operator L " has a regular sin- gularity at So with exponents le1 , le . = 0 By passing from the equation Lf = 0 to the equation L ' ' ' f ...
Page 1527
... equation we must consequently use some of the theory of equations with irregular singular points . It is most convenient to take the equation Lf ( d / dz ) 2f + p ( z ) ( d / dz ) f + q ( z ) ƒ = 0 to have an irregular singularity of ...
... equation we must consequently use some of the theory of equations with irregular singular points . It is most convenient to take the equation Lf ( d / dz ) 2f + p ( z ) ( d / dz ) f + q ( z ) ƒ = 0 to have an irregular singularity of ...
Page 1556
... 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 equation τf = 0 . G15 ...
... 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 equation τf = 0 . G15 ...
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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