Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1327
... obtained from 7 by imposing a real symmetric set of boundary con- ditions , a further simplification can be obtained by noticing that the solutions of the equation ( 7 * —Ã ) σ = 0 are complex conjugates of the solutions of the ...
... obtained from 7 by imposing a real symmetric set of boundary con- ditions , a further simplification can be obtained by noticing that the solutions of the equation ( 7 * —Ã ) σ = 0 are complex conjugates of the solutions of the ...
Page 1617
... obtained by the imposition of separated boundary conditions , and let { g } be the orthonormal eigenfunctions obtained from the operator — ( d / dt ) 2 by the imposition of the same boundary conditions on an interval [ a , b ] . Let f ...
... obtained by the imposition of separated boundary conditions , and let { g } be the orthonormal eigenfunctions obtained from the operator — ( d / dt ) 2 by the imposition of the same boundary conditions on an interval [ a , b ] . Let f ...
Page 1619
... obtained by the imposition of a boundary condition at zero will consist of a continuous spectrum covering the positive real semi - axis , and a sequence of eigenvalues with simple normalized eigenfunctions { fn } . Let f ( t , 2 ) be a ...
... obtained by the imposition of a boundary condition at zero will consist of a continuous spectrum covering the positive real semi - axis , and a sequence of eigenvalues with simple normalized eigenfunctions { fn } . Let f ( t , 2 ) be a ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero