Linear Operators, Part 2 |
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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 1305
If B ( A ) O is not a boundary condition either at a or at b ( so that , by Theorem 19 , the equation B ( f ) = 0 ) may be written as B ) B2 ( / ) , where B , and B , are non - zero boundary values at a and b respectively ) , then B ( f ) ...
If B ( A ) O is not a boundary condition either at a or at b ( so that , by Theorem 19 , the equation B ( f ) = 0 ) may be written as B ) B2 ( / ) , where B , and B , are non - zero boundary values at a and b respectively ) , then B ( f ) ...
Page 1307
2 boundary values C1 , C2 , D1 , D , where C1 , C , are boundary values at a and D2 , D , are boundary values at b , such that ( tf , g ) - ( 1 , tg ) = C ( C2 ( g ) -C2 ( 1 ) C ( 8 ) + D ( 1 ) D2 ( g ) – D2 ( 1 ) D , ( 8 ) , f , ge D ...
2 boundary values C1 , C2 , D1 , D , where C1 , C , are boundary values at a and D2 , D , are boundary values at b , such that ( tf , g ) - ( 1 , tg ) = C ( C2 ( g ) -C2 ( 1 ) C ( 8 ) + D ( 1 ) D2 ( g ) – D2 ( 1 ) D , ( 8 ) , f , ge D ...
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Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
13 other sections not shown
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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero