Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 66
Page 859
... example , the classes con- sisting of the bounded functions on a set , the bounded continuous functions on a topological space , functions of bounded variation , almost periodic functions , functions with n continuous derivatives , and ...
... example , the classes con- sisting of the bounded functions on a set , the bounded continuous functions on a topological space , functions of bounded variation , almost periodic functions , functions with n continuous derivatives , and ...
Page 909
... examples of a bounded normal operator is the operator T defined by the formula ( Tx ) ( 2 ) = 2x ( 2 ) , x = L2 ( S , B , μ ) ... example just given is typical of the structure of every normal operator . More explicitly , if T is a normal ...
... examples of a bounded normal operator is the operator T defined by the formula ( Tx ) ( 2 ) = 2x ( 2 ) , x = L2 ( S , B , μ ) ... example just given is typical of the structure of every normal operator . More explicitly , if T is a normal ...
Page 1782
... example , any one of the following norms defines the product topology in X. i = = \ x11 + \ x22 + • | x11 + x 2 2 + ... + | xn | n ( i ) │ [ x1 , ... , x , ] | ( ii ) | [ x1 , x ,, ] [ = | ( iii ) | [ x1 , .. xn ] = sup x 1≤i≤n ...
... example , any one of the following norms defines the product topology in X. i = = \ x11 + \ x22 + • | x11 + x 2 2 + ... + | xn | n ( i ) │ [ x1 , ... , x , ] | ( ii ) | [ x1 , x ,, ] [ = | ( iii ) | [ x1 , .. xn ] = sup x 1≤i≤n ...
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