Linear Operators: Spectral theory |
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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 ( q ) CF. PROOF . Let N be a neighborhood of o ...
... 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 ( q ) CF. PROOF . Let N be a neighborhood of o ...
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 a , ( t ) and ẞ , ( 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 a , ( t ) and ẞ , ( 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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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