Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 990
... determined by the char- acters in any neighborhood of its spectral set . Conversely , if q is in the L - closed linear manifold determined by the characters in some closed set F in R then o ( p ) C F. PROOF . Let N be a neighborhood of ...
... determined by the char- acters in any neighborhood of its spectral set . Conversely , if q is in the L - closed linear manifold determined by the characters in some closed set F in R then o ( p ) C F. PROOF . Let N be a neighborhood of ...
Page 1321
... determined by the jump equations and by the boundary conditions defining T. PROOF . We have seen in the derivation of Theorem 8 that the functions x , ( t ) and B , ( t ) are uniquely determined by the jump equa- tions and by the ...
... determined by the jump equations and by the boundary conditions defining T. PROOF . We have seen in the derivation of Theorem 8 that the functions x , ( t ) and B , ( t ) are uniquely determined by the jump equa- tions and by the ...
Page 1323
... determined by separated sets of boundary conditions . Then u + v = k , μ * + v * = k * , and the coefficients y , and y ' , are uniquely determined by the jump equations . By Lemmas 1 and 2 , p * + q * = n + k * , u * + v * = p * + q ...
... determined by separated sets of boundary conditions . Then u + v = k , μ * + v * = k * , and the coefficients y , and y ' , are uniquely determined by the jump equations . By Lemmas 1 and 2 , p * + q * = n + k * , u * + v * = p * + q ...
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