Linear Operators: Spectral theory |
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Page 940
... finite dimensional if its set { ƒ3 \ s e G } of translates is a finite dimensional vector space of functions . = The spectral theorem will be used in the proof of the following theorem and so the field of scalars is taken to be the ...
... finite dimensional if its set { ƒ3 \ s e G } of translates is a finite dimensional vector space of functions . = The spectral theorem will be used in the proof of the following theorem and so the field of scalars is taken to be the ...
Page 1092
... finite number N of non - zero eigenvalues , we write λ „ ( T ) = 0 , n > N ) . Then , for each positive integer m ... dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain and ...
... finite number N of non - zero eigenvalues , we write λ „ ( T ) = 0 , n > N ) . Then , for each positive integer m ... dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain and ...
Page 1146
... finite dimensional representation of a compact group G is a direct sum of irreducible representations . This theorem shows that in studying finite dimensional represen- tations of a compact group G we may , without loss of generality ...
... finite dimensional representation of a compact group G is a direct sum of irreducible representations . This theorem shows that in studying finite dimensional represen- tations of a compact group G we may , without loss of generality ...
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