Linear Operators: Spectral theory |
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Page 916
... multiplicity k . If u ( e ) > 0 for all k , the representation is said to have infinite multiplicity . Two ordered repre- sentations U and U of relative to T and I respectively , with measures and μ , and multiplicity sets { e } and { e } ...
... multiplicity k . If u ( e ) > 0 for all k , the representation is said to have infinite multiplicity . Two ordered repre- sentations U and U of relative to T and I respectively , with measures and μ , and multiplicity sets { e } and { e } ...
Page 1091
... multiplicity . Then there exist enumerations Am ( Tn ) of the non - zero eigenvalues of Tn with repetitions according to multiplicity , such that lim Am ( Tn ) = λm ( T ) , the limit being uniform in m . Εκ m≥ 1 , PROOF . Choose a ...
... multiplicity . Then there exist enumerations Am ( Tn ) of the non - zero eigenvalues of Tn with repetitions according to multiplicity , such that lim Am ( Tn ) = λm ( T ) , the limit being uniform in m . Εκ m≥ 1 , 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 U of relative to T and I respectively , with measures μ 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 representations U and U of relative to T and I respectively , with measures μ and μ , and multiplicity sets { e , } and ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero