Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 940
... finite dimensional if its set { fs se 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 field of ...
... finite dimensional if its set { fs se 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 field of ...
Page 1092
... finite number N of non - zero eigenvalues , we write λ ( T ) = 0 , n > N ) . Then , for each positive integer m ( a ) ... 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 ( a ) ... 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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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 Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm 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 transform unique unitary vanishes vector zero