Linear Operators: Spectral theory |
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Page 1092
... finite number N of non - zero eigenvalues , we write 2 „ ( 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 2 „ ( 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 1459
... finite below any finite 2 . PROOF . We use the notations of the proof of Theorem 8. By Lemma 29 and Theorem 28 it is sufficient to show that t ' is finite below 10 in order to conclude that 7 is finite below 2. But it was shown in the ...
... finite below any finite 2 . PROOF . We use the notations of the proof of Theorem 8. By Lemma 29 and Theorem 28 it is sufficient to show that t ' is finite below 10 in order to conclude that 7 is finite below 2. But it was shown in the ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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 complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero