Linear Operators: Spectral theory |
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Page 1040
y ( 2 ) is analytic even at 1 = hm . It will now be shown that yo ( 2 ) a - 2 2N Eām ; T ) * R ( ā ; T ) * y vanishes which will prove that y ( a ) is analytic at all the points à am , so that y ( 2 ) can only fail to be analytic at the ...
y ( 2 ) is analytic even at 1 = hm . It will now be shown that yo ( 2 ) a - 2 2N Eām ; T ) * R ( ā ; T ) * y vanishes which will prove that y ( a ) is analytic at all the points à am , so that y ( 2 ) can only fail to be analytic at the ...
Page 1102
The determinant det ( I + zTn ) is an analytic ( and even a polynomial ) function of z , if T , operates in finite - dimensional space , and hence more generally if T , has a finite - dimensional range .
The determinant det ( I + zTn ) is an analytic ( and even a polynomial ) function of z , if T , operates in finite - dimensional space , and hence more generally if T , has a finite - dimensional range .
Page 1492
.Qx ( 2 ) analytic in U. ( The set e , is that isolated set of points in U in which two or more of these distinct analytic functions take on the same value . ) For 1 in U - o , the eigenvalues 4i ( 2 ) , i = 1 , ... , k , are distinct ...
.Qx ( 2 ) analytic in U. ( The set e , is that isolated set of points in U in which two or more of these distinct analytic functions take on the same value . ) For 1 in U - o , the eigenvalues 4i ( 2 ) , i = 1 , ... , k , are distinct ...
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Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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