Linear Operators: Spectral theory |
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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 1307
2 boundary values C1 , C2 , D2 , D , where C1 , C , are boundary values at a and D , D , are boundary values at b ... Let A be any boundary value for T. Since t is real , D ( T_ ( 7 ) ) is closed under the formation of complex ...
2 boundary values C1 , C2 , D2 , D , where C1 , C , are boundary values at a and D , D , are boundary values at b ... Let A be any boundary value for T. Since t is real , D ( T_ ( 7 ) ) is closed under the formation of complex ...
Page 1471
τ 2 = d1 , , real , > = 21 , 0 , real , if t has no boundary values at b ; while if t has boundary values at b , τ we may find two real boundary values D1 , D , for T , at b , such that ( taf , g ) - ( 1 , T28 ) = D. ( / ) D2 ( g ) - D2 ...
τ 2 = d1 , , real , > = 21 , 0 , real , if t has no boundary values at b ; while if t has boundary values at b , τ we may find two real boundary values D1 , D , for T , at b , such that ( taf , g ) - ( 1 , T28 ) = D. ( / ) D2 ( g ) - D2 ...
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Contents
8 | 876 |
859 | 885 |
extensive presentation of applications of the spectral theorem | 911 |
Copyright | |
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additive adjoint adjoint operator algebra analytic assume 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 domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero