Linear Operators, Part 2 |
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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 ) 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 ( p ) 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 x , ( 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 x , ( 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 | 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