Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 84
Page 890
... formula ( vi ) , but in this situation it is necessary to define the integral appearing in ( vi ) and to define the algebra of scalar functions f to which the formula may be applied . One class of scalar functions f , other than ...
... formula ( vi ) , but in this situation it is necessary to define the integral appearing in ( vi ) and to define the algebra of scalar functions f to which the formula may be applied . One class of scalar functions f , other than ...
Page 1089
... formula " for the eigenvalues of a com- pact operator , given as Theorem X.4.3 . Q.E.D. It will be convenient in what follows to adopt the formula of Lemma 2 as a definition of μ „ ( T ) in case T is not compact . Note that | T | = μ1 ...
... formula " for the eigenvalues of a com- pact operator , given as Theorem X.4.3 . Q.E.D. It will be convenient in what follows to adopt the formula of Lemma 2 as a definition of μ „ ( T ) in case T is not compact . Note that | T | = μ1 ...
Page 1363
... formula 1 E ( ( λ1 , λ2 ) ) ƒ = lim lim Σπί λ2 + 8 + 0-3 0-8 [ R ( 2 - iɛ ; T ) -R ( λ + ie ; T ) ] fdλ . The problem we face is that of passing from this latter formula in- volving the resolvent to a formula involving the individual ...
... formula 1 E ( ( λ1 , λ2 ) ) ƒ = lim lim Σπί λ2 + 8 + 0-3 0-8 [ R ( 2 - iɛ ; T ) -R ( λ + ie ; T ) ] fdλ . The problem we face is that of passing from this latter formula in- volving the resolvent to a formula involving the individual ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
37 other sections not shown
Other editions - View all
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 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