Linear Operators: Spectral theory |
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Page 916
... multiplicity k . If μ ( ex ) > 0 for all k , the representation is said to have infinite multiplicity . Two ordered repre- sentations U and U of relative to T and T respectively , with measures and μ , and multiplicity sets { e } and ...
... multiplicity k . If μ ( ex ) > 0 for all k , the representation is said to have infinite multiplicity . Two ordered repre- sentations U and U of relative to T and T respectively , with measures and μ , and multiplicity sets { e } and ...
Page 1091
... multiplicity . Then there exist enumerations Am ( T ) of the non - zero eigenvalues of Tn , with repetitions according to multiplicity , such that lim λm ( Tn ) = λm ( T ) , 248 the limit being uniform in m . m≥ 1 , Εκ PROOF . Choose a ...
... multiplicity . Then there exist enumerations Am ( T ) of the non - zero eigenvalues of Tn , with repetitions according to multiplicity , such that lim λm ( Tn ) = λm ( T ) , 248 the limit being uniform in m . m≥ 1 , Εκ PROOF . Choose a ...
Page 1217
... multiplicity k . If μ ( ex ) > 0 for all k , the representation is said to have infinite multiplicity . Two ordered representations U and Ũ of H relative to T and Ĩ respectively , with measures μ and μ , and multiplicity sets { e ...
... multiplicity k . If μ ( ex ) > 0 for all k , the representation is said to have infinite multiplicity . Two ordered representations U and Ũ of H relative to T and Ĩ respectively , with measures μ and μ , and multiplicity sets { e ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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59 other sections not shown
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