Linear Operators: Spectral theory |
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Page 1383
... eigenfunctions being complete . With boundary condi- tions A and C , the unique solution of 730 = λo satisfying the boundary lo condition T3σ = λo is sin √t . With boundary conditions A , the eigen- values are consequently to be ...
... eigenfunctions being complete . With boundary condi- tions A and C , the unique solution of 730 = λo satisfying the boundary lo condition T3σ = λo is sin √t . With boundary conditions A , the eigen- values are consequently to be ...
Page 1386
... eigenfunction associated with the eigenvalue = -1 / k2 is 21/2 k - 1 / 2 / k . This fact has already been noted ; but the ... eigenfunctions are , say , Laguerre polynomials , we will find considerable use for the general method of ...
... eigenfunction associated with the eigenvalue = -1 / k2 is 21/2 k - 1 / 2 / k . This fact has already been noted ; but the ... eigenfunctions are , say , Laguerre polynomials , we will find considerable use for the general method of ...
Page 1617
... eigen- functions obtained by the impositions of separated boundary con- ditions ( a ) there exist continuous functions ... eigenfunctions obtained from the operator — ( d / dt ) 2 by the imposition of the same boundary conditions on an ...
... eigen- functions obtained by the impositions of separated boundary con- ditions ( a ) there exist continuous functions ... eigenfunctions obtained from the operator — ( d / dt ) 2 by the imposition of the same boundary conditions on an ...
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