Linear Operators: Spectral theory |
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Results 1-3 of 83
Page 972
... equal to unity , it follows from Plan- cherel's theorem that { μ ( e + p ) } 2 = { u ( e ) } 2 . Hence if μ ( e ) < ∞ , we have proved that μ ( e + p ) is also finite and equals u ( e ) . If u ( e + p ) were known to be finite we would ...
... equal to unity , it follows from Plan- cherel's theorem that { μ ( e + p ) } 2 = { u ( e ) } 2 . Hence if μ ( e ) < ∞ , we have proved that μ ( e + p ) is also finite and equals u ( e ) . If u ( e + p ) were known to be finite we would ...
Page 1177
... equal to 1 for 1 ≤ | § | ≤ 2 , identically equal to zero for │§ | ≤ 1/2 or │§ | ≥ 3 , chosen so that its integral and first few moments are zero . Let Ê ( § ) be the vector whose nth component is q ( 2 " ) ; R is then a vector ...
... equal to 1 for 1 ≤ | § | ≤ 2 , identically equal to zero for │§ | ≤ 1/2 or │§ | ≥ 3 , chosen so that its integral and first few moments are zero . Let Ê ( § ) be the vector whose nth component is q ( 2 " ) ; R is then a vector ...
Page 1396
... equal . Moreover , all the self adjoint extensions of To ( t ) have the same set of non - isolated points , and this set is equal to σ , ( T ) . PROOF . The second assertion follows immediately from Theorem 5 and Corollary 4. In proving ...
... equal . Moreover , all the self adjoint extensions of To ( t ) have the same set of non - isolated points , and this set is equal to σ , ( T ) . PROOF . The second assertion follows immediately from Theorem 5 and Corollary 4. In proving ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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Common terms and phrases
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 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 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 PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero