Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 60
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 UA - 1T , UU * = A - 1 A2A - 1 I , then U is unitary , and T = AU . Let B1 = 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 UA - 1T , UU * = A - 1 A2A - 1 I , then U is unitary , and T = AU . Let B1 = U - 1AP - 1 . Then ...
Page 1184
... singular integrals . Singular integrals of Hilbert - Calderón- Zygmund type may be shown under suitable hypotheses to map functions satisfying a Hölder condition of exponent 0 < ɛ < 1 into functions of the same sort . Singular integrals ...
... singular integrals . Singular integrals of Hilbert - Calderón- Zygmund type may be shown under suitable hypotheses to map functions satisfying a Hölder condition of exponent 0 < ɛ < 1 into functions of the same sort . Singular integrals ...
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 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
57 other sections not shown
Other editions - View all
Common terms and phrases
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 Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero