Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
From inside the book
Results 1-3 of 66
Page 1297
Q.E.D. We now turn to a discussion of the specific form assumed in the present case by the abstract " boundary values " introduced in the last chapter . We shall see that the discussion leads us to a number of results about deficiency ...
Q.E.D. We now turn to a discussion of the specific form assumed in the present case by the abstract " boundary values " introduced in the last chapter . We shall see that the discussion leads us to a number of results about deficiency ...
Page 1305
If B ( 1 ) O is not a boundary condition either at a or at b ( so that , by Theorem 19 , the equation B ( A ) = 0 may be written as B. ( t ) = B2 ( 1 ) , where B , and B , are non - zero boundary values at a and b respectively ) ...
If B ( 1 ) O is not a boundary condition either at a or at b ( so that , by Theorem 19 , the equation B ( A ) = 0 may be written as B. ( t ) = B2 ( 1 ) , where B , and B , are non - zero boundary values at a and b respectively ) ...
Page 1307
boundary values C ,, C2 , D1 , D , where C1 , C , are boundary values at a and D. , D , are boundary values at b , such that ( 7 ) ... so the functional A defined by the formula Ā ( f ) = A ( 5 ) is also a boundary value for t .
boundary values C ,, C2 , D1 , D , where C1 , C , are boundary values at a and D. , D , are boundary values at b , such that ( 7 ) ... so the functional A defined by the formula Ā ( f ) = A ( 5 ) is also a boundary value for t .
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