Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 90
Page 948
... on R , = = S2S and , i { u1 u2 } = T ( u1 , u2 ) C W ( U1 , U2 ) u2 € V. This proves that is continuous . From the ... in R then h ( s ) -s , and so sh ( s ) = 0 for s in a dense set R and thus identically on S. Consequently h ( s ) is ...
... on R , = = S2S and , i { u1 u2 } = T ( u1 , u2 ) C W ( U1 , U2 ) u2 € V. This proves that is continuous . From the ... in R then h ( s ) -s , and so sh ( s ) = 0 for s in a dense set R and thus identically on S. Consequently h ( s ) is ...
Page 1159
... of R into R. space Next we shall show that κ ( R ) is dense in the Ê . If not , then by applying Lemma 4.2 to R , we find that there exists a function HЄ L1 L2 ( R ) with H│20 but such that fH vanishes on κ ( R ) . If h = T1H € L ( R ) ...
... of R into R. space Next we shall show that κ ( R ) is dense in the Ê . If not , then by applying Lemma 4.2 to R , we find that there exists a function HЄ L1 L2 ( R ) with H│20 but such that fH vanishes on κ ( R ) . If h = T1H € L ( R ) ...
Page 1249
... R ( A ' ) = 1 is dense in R ( A ) . Let P1 be the isometric extension of Po to R ( A ) and let E be the perpendicular projection of H onto R ( A ) . If we define P = P1E , then P is a partial isometry whose initial domain is R ( A ) ...
... R ( A ' ) = 1 is dense in R ( A ) . Let P1 be the isometric extension of Po to R ( A ) and let E be the perpendicular projection of H onto R ( A ) . If we define P = P1E , then P is a partial isometry whose initial domain is R ( A ) ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
45 other sections not shown
Other editions - View all
Common terms and phrases
A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero