Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1343
... sufficiently close to ¿ , σ ( M ( 2 ) ) ~ U is non - void . Thus if n ( 2 ) denotes the number of distinct points in the spectrum of M ( 1 ) , the sets { λ € σn ( λ ) ≥ s } are relatively open in σo , and hence the sets b { λ € σon ( λ ) ...
... sufficiently close to ¿ , σ ( M ( 2 ) ) ~ U is non - void . Thus if n ( 2 ) denotes the number of distinct points in the spectrum of M ( 1 ) , the sets { λ € σn ( λ ) ≥ s } are relatively open in σo , and hence the sets b { λ € σon ( λ ) ...
Page 1450
... sufficiently small bo , and if So is \ q ( t ) | -1⁄2 dt < ∞ 0 for sufficiently small b , then σ ( t ) is void . ← ( d ) If q ( t ) sufficiently small t , ∞ as t → 0 , q ( t ) is monotone decreasing for g ' ( t ) q ( t ) ' q ( t ) 3 ...
... sufficiently small bo , and if So is \ q ( t ) | -1⁄2 dt < ∞ 0 for sufficiently small b , then σ ( t ) is void . ← ( d ) If q ( t ) sufficiently small t , ∞ as t → 0 , q ( t ) is monotone decreasing for g ' ( t ) q ( t ) ' q ( t ) 3 ...
Page 1760
... sufficiently small positive a ≤a ( k ) , the mapping I - ¿ S , has a range dense in Â1⁄4 ( C ) . k π Suppose that ( v ) is false , but that ( vii ) has been established . Since ( v ) is false , and since D ( S ) = D ( W ) , there ...
... sufficiently small positive a ≤a ( k ) , the mapping I - ¿ S , has a range dense in Â1⁄4 ( C ) . k π Suppose that ( v ) is false , but that ( vii ) has been established . Since ( v ) is false , and since D ( S ) = D ( W ) , there ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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