Linear Operators, Part 2 |
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Page 944
... dimensional space and thus that Tg is a finite dimensional function . Q.E.D. In the case of compact Abelian groups , Theorem 4 may be sharpened to some extent . 5 DEFINITION . If G is an Abelian group , then a character of G is a ...
... dimensional space and thus that Tg is a finite dimensional function . Q.E.D. In the case of compact Abelian groups , Theorem 4 may be sharpened to some extent . 5 DEFINITION . If G is an Abelian group , then a character of G is a ...
Page 1092
... dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain and range . Note that if T has finite - dimensional range , T = ET , where E is the orthogonal projection on the range of T ...
... dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain and range . Note that if T has finite - dimensional range , T = ET , where E is the orthogonal projection on the range of T ...
Page 1146
... 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 , confine ...
... 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 , confine ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant 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(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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero