Linear Operators, Part 2 |
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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 condition 73σ = 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 condition 73σ = λo is sin √t . With boundary conditions A , the eigen- values are consequently to be ...
Page 1520
... eigenfunctions of T are the even functions satisfying the self adjoint set 4 ( f ) B_ ( f ) of boundary con- ditions ... eigenfunction of the self adjoint restriction S of T1 ( L ) determined by this latter pair of boundary conditions ...
... eigenfunctions of T are the even functions satisfying the self adjoint set 4 ( f ) B_ ( f ) of boundary con- ditions ... eigenfunction of the self adjoint restriction S of T1 ( L ) determined by this latter pair of boundary conditions ...
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 | 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