Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
From inside the book
Results 1-3 of 85
Page 890
... then the function E is a resolution of the identity for T and the operational calculus is given by the formula ( vi ) ( T ) = Soxo , 7 ( 2 ) E ( ) , where the integral is defined as the finite sum L = 1 / 12 ; ) E ( ) :) .
... then the function E is a resolution of the identity for T and the operational calculus is given by the formula ( vi ) ( T ) = Soxo , 7 ( 2 ) E ( ) , where the integral is defined as the finite sum L = 1 / 12 ; ) E ( ) :) .
Page 1288
( Green's formula ) Lett be a regular or irregular formal differential operator of order n on the finite closed interval I = [ a , b ] . If , ge ( ) , then So ( 7198 ) g ( + ) dt = S010 ) ( 7 * g ) t } dt + Fo ( 1,6 ) –Fell , g ) .
( Green's formula ) Lett be a regular or irregular formal differential operator of order n on the finite closed interval I = [ a , b ] . If , ge ( ) , then So ( 7198 ) g ( + ) dt = S010 ) ( 7 * g ) t } dt + Fo ( 1,6 ) –Fell , g ) .
Page 1363
basis for this formula is found in Theorem XII.2.10 which asserts that the projection in the resolution of the identity for T corresponding to ( 21,1 % ) may be calculated from the resolvent by the formula 1 E ( ( 22 , 22 ) ) } = lim ...
basis for this formula is found in Theorem XII.2.10 which asserts that the projection in the resolution of the identity for T corresponding to ( 21,1 % ) may be calculated from the resolvent by the formula 1 E ( ( 22 , 22 ) ) } = lim ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
Common terms and phrases
additive adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero