Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 81
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 ( y ) CF. Φ = 0 for PROOF . Let N be a ...
... 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 ( y ) CF. Φ = 0 for PROOF . Let N be a ...
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 y1 , 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 y1 , 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 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero