Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 62
Page 1099
... singular matrices , it is sufficient to consider the case in which T is non - singular . Then A = ( TT * ) 1/2 is also non - singular and if U = A - 1T , UU * = A - 142A - 1 I , then U is unitary , and TAU . Let Bo = U - 1AP - 1 . Then ...
... singular matrices , it is sufficient to consider the case in which T is non - singular . Then A = ( TT * ) 1/2 is also non - singular and if U = A - 1T , UU * = A - 142A - 1 I , then U is unitary , and TAU . Let Bo = U - 1AP - 1 . Then ...
Page 1505
... singular point at which the exponents are zero and one . If Lf 0 is a differential equation with rational ... singular point , singular point of order k , regular singular point , indicial equation , and exponents to the point at ...
... singular point at which the exponents are zero and one . If Lf 0 is a differential equation with rational ... singular point , singular point of order k , regular singular point , indicial equation , and exponents to the point at ...
Page 1919
... Singular element in a B - algebra IX.1.2 ( 861 ) Singular element in a ring , ( 40 ) non - singular operator , ( 45 ) Singular set function , definition , III.4.12 ( 131 ) derivatives of , III.12.6 ( 214 ) Lebesgue decomposition theorem ...
... Singular element in a B - algebra IX.1.2 ( 861 ) Singular element in a ring , ( 40 ) non - singular operator , ( 45 ) Singular set function , definition , III.4.12 ( 131 ) derivatives of , III.12.6 ( 214 ) Lebesgue decomposition theorem ...
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