Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1092
... finite number N of non - zero eigenvalues , we write λ , ( T ) = 0 , n > N ) . Then , for each positive integer m ... finite- dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain ...
... finite number N of non - zero eigenvalues , we write λ , ( T ) = 0 , n > N ) . Then , for each positive integer m ... finite- dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain ...
Page 1147
... finite set , then any complete set of representations of G is countable . A complete set of representations of a finite group is finite . DEFINITION : A class function on a compact group G is an element f of L2 ( G ) such that f ( h ) ...
... finite set , then any complete set of representations of G is countable . A complete set of representations of a finite group is finite . DEFINITION : A class function on a compact group G is an element f of L2 ( G ) such that f ( h ) ...
Page 1460
... finite below 2 , and the leading coefficient of t + 1 never vanishes , T + T1 is finite below λ . = PROOF . It is clear that we may suppose without loss of generality that 20. By Corollary 24 ( b ) , Corollary XII.4.13 , and Corollary ...
... finite below 2 , and the leading coefficient of t + 1 never vanishes , T + T1 is finite below λ . = PROOF . It is clear that we may suppose without loss of generality that 20. By Corollary 24 ( b ) , Corollary XII.4.13 , and Corollary ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum 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(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero