Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 36
Page 1017
... polynomial of the operator . ( b ) The trace of an operator in En is equal to the sum of the numbers in the spectrum of the operator , if each number is counted according to its multiplicity as a root of the characteristic polynomial ...
... polynomial of the operator . ( b ) The trace of an operator in En is equal to the sum of the numbers in the spectrum of the operator , if each number is counted according to its multiplicity as a root of the characteristic polynomial ...
Page 1196
... polynomial + α11 + . I + α1T + ... + a " then f ( T ) is the polynomial a , I + a , T + ... + x , T " as defined in Definition 1.1 or as in Definition VII.9.6 . This is the case , as will be shown in Corollary 8 below , so that the ...
... polynomial + α11 + . I + α1T + ... + a " then f ( T ) is the polynomial a , I + a , T + ... + x , T " as defined in Definition 1.1 or as in Definition VII.9.6 . This is the case , as will be shown in Corollary 8 below , so that the ...
Page 1276
... polynomials determined by orthonormalizing the se- quence 1 , t , t2 , ... of elementary polynomials with respect to μ . That is , let Pn be the sequence of polynomials determined by the conditions n ( i ) P is a polynomial of order n ...
... polynomials determined by orthonormalizing the se- quence 1 , t , t2 , ... of elementary polynomials with respect to μ . That is , let Pn be the sequence of polynomials determined by the conditions n ( i ) P is a polynomial of order 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