Linear Operators: Spectral operators |
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Page 2260
( iii ' ) There is a constant M depending only on S such that Sors \ R * ( 1 , yo , yo ) – R – ( , 46 , yoll ds S M 196 / | yol , Yo Y. , y * EY , O ( S2 ) where 8 is the arc length along C. We now note ( cf. Theorem VII.9.5 and formula ...
( iii ' ) There is a constant M depending only on S such that Sors \ R * ( 1 , yo , yo ) – R – ( , 46 , yoll ds S M 196 / | yol , Yo Y. , y * EY , O ( S2 ) where 8 is the arc length along C. We now note ( cf. Theorem VII.9.5 and formula ...
Page 2425
If we put ( 33 ) ( ( B ) } ( ) = ** B ( s , 0 ) f ( o ) do , S - 0 it follows from Lemma 5 and from ( 31 ) and ( 32 ) that there exists a finite constant Ny , B ) depending only on y and B such that +00 1/2 + 1/2 ( 34 ) { S : 1 ( 1 \ B ) ...
If we put ( 33 ) ( ( B ) } ( ) = ** B ( s , 0 ) f ( o ) do , S - 0 it follows from Lemma 5 and from ( 31 ) and ( 32 ) that there exists a finite constant Ny , B ) depending only on y and B such that +00 1/2 + 1/2 ( 34 ) { S : 1 ( 1 \ B ) ...
Page 2441
This shows that there exists a finite absolute constant c ' such that I ( x ) = c ' ( 1 + 10l ) -n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite constant M " independent of a such that E OV 4 OV 4 22 V ...
This shows that there exists a finite absolute constant c ' such that I ( x ) = c ' ( 1 + 10l ) -n + 1 . Using this inequality and using ( 37 ) , we see that there exists a finite constant M " independent of a such that E OV 4 OV 4 22 V ...
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Contents
SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1931 |
Copyright | |
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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero