Linear Operators: Spectral operators |
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Page 2017
and the fraction in the inequality ( i ) of Theorem 6 is 1si - s ? l2 + 2 | 818212 { ( si
- $ ) * + 16s1 s } 1 / 2 which is bounded on all of Rn . Thus As has a resolution of
the identity . Furthermore , the set Sy is the null set { s | 81 = 82 = 0 } , so that Ag ...
and the fraction in the inequality ( i ) of Theorem 6 is 1si - s ? l2 + 2 | 818212 { ( si
- $ ) * + 16s1 s } 1 / 2 which is bounded on all of Rn . Thus As has a resolution of
the identity . Furthermore , the set Sy is the null set { s | 81 = 82 = 0 } , so that Ag ...
Page 2190
Thus for some constant K we have S ( f ) = K \ f and to prove the final inequality of
the present theorem it will suffice to prove that fe = S ( F ) . Since both terms in this
inequality are continuous functions of f , it will suffice to prove it for every ...
Thus for some constant K we have S ( f ) = K \ f and to prove the final inequality of
the present theorem it will suffice to prove that fe = S ( F ) . Since both terms in this
inequality are continuous functions of f , it will suffice to prove it for every ...
Page 2221
Since \ f ( TQ ) | S 4M sup 15 ( 1 ) | SL , LEV the inequality \ f ( Ta ) gn ( T ) x – f (
Ta ) gn ( Twx | SL \ gn ( T ) x — 9n ( Ta ) x | shows that lim f ( T ) gn ( Ta XVII . 4 . 3
2221 STRONG LIMITS OF SPECTRAL OPERATORS Strong Limits of Spectral ...
Since \ f ( TQ ) | S 4M sup 15 ( 1 ) | SL , LEV the inequality \ f ( Ta ) gn ( T ) x – f (
Ta ) gn ( Twx | SL \ gn ( T ) x — 9n ( Ta ) x | shows that lim f ( T ) gn ( Ta XVII . 4 . 3
2221 STRONG LIMITS OF SPECTRAL OPERATORS Strong Limits of Spectral ...
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