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 ) CF. = 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 ) CF. = 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 ( t ) and ẞ , ( t ) are uniquely determined by the jump equa- tions and by the boundary ...
... 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 ( t ) and ẞ , ( t ) are uniquely determined by the jump equa- tions and by the boundary ...
Page 1323
... determined by separated sets of boundary conditions . Then μ + 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 μ + 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
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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 Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined 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 linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero