Linear Operators: Spectral theory |
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Page 950
... measure is unique up to multiplication by positive numbers , and is called Haar measure . In the case R ( ∞ , ∞ ) , the Haar measure may be taken to be Lebesgue measure : in the case of a compact group , its existence and uniqueness ...
... measure is unique up to multiplication by positive numbers , and is called Haar measure . In the case R ( ∞ , ∞ ) , the Haar measure may be taken to be Lebesgue measure : in the case of a compact group , its existence and uniqueness ...
Page 1210
... measure space . Let E be the resolution of the identity for T. We assume that there exists an increasing sequence ... Lebesgue measure . We will see that every function in D ( T ) is 1210 XII . UNBOUNDED OPERATORS IN HILBERT SPACE XII.3.7.
... measure space . Let E be the resolution of the identity for T. We assume that there exists an increasing sequence ... Lebesgue measure . We will see that every function in D ( T ) is 1210 XII . UNBOUNDED OPERATORS IN HILBERT SPACE XII.3.7.
Page 1213
... Lebesgue measure , and W will , for almost all 2 , be square in- tegrable over every compact subset of S. In this case the limit F of the preceding definition is independent of the sequence { S } provided that the sets S are compact . n ...
... Lebesgue measure , and W will , for almost all 2 , be square in- tegrable over every compact subset of S. In this case the limit F of the preceding definition is independent of the sequence { S } provided that the sets S are compact . n ...
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