Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 35
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 ...
... 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 ...
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 ...
... 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 ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Copyright | |
29 other sections not shown
Other editions - View all
Common terms and phrases
A₁ 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 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 subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero