DAIDEN.IN Book Archive > Analytic > Download PDF by Boris Nikolaevič Apanasov (auth.), Julian Ławrynowicz (eds.): Analytic Functions Błażejewko 1982: Proceedings of a

Download PDF by Boris Nikolaevič Apanasov (auth.), Julian Ławrynowicz (eds.): Analytic Functions Błażejewko 1982: Proceedings of a

By Boris Nikolaevič Apanasov (auth.), Julian Ławrynowicz (eds.)

ISBN-10: 3540127127

ISBN-13: 9783540127123

ISBN-10: 3540386971

ISBN-13: 9783540386971

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Extra resources for Analytic Functions Błażejewko 1982: Proceedings of a Conference held in Błażejewko, Poland, August 19–27, 1982

Sample text

Operator-valued Pick's conditions and holomorphicity, Pacific J. Math. 98 (1982), 295-311. : Monotone MatriX Functions and Analytic Continuation, SpringerVerlag, New York, 1974. : On quadratic and bilinear forms in function theory, Proc. London Math. Soc. (3) 44 (1982), 554-576. : 527-531. Pick's conditions and analyticity, Pacific J. Math. A. ABOUT THE EQUALITY BETWEEN THE p-MODULE AND THE p-CAPACITY IN an Petru Caraman .. ~w, Contents Introduction ,. p-module and p-~apa~i ty' i~ the ~a;e' of ;p~n' s~t; • D~ n ' 2.

E(r ,r ) = lXir1 r }. 1 have Yet, all the points the form (11), i . e. th zero. Thus, the hypotheses of the preceding theorem, are satisfied what, by (23), yields o. 54 Petru Caraman Hence (24) cap [E',E'(r ,oo) ,D) 1 P = = inf u JlvulPdm D capp[E',E'(r1,r2),DnE'(r2}] = = inf J IVulPdm u DnE'(r ) 2 O. If we denote by U(E ,E ,D} the class of admissible functions for o 1 cap (E ,E ,D), then for r

Next, by Theorem 1 and 2 in Fuglede's paper [10], r 41 About the Equality between the p-Module and the p-Capacity in M p r :;; 0 1: M r m=1 p m and =0 n R whence Mr":;;Mr:;;Mr"+Mr =Mr" p p p po p' 1-1 r". p Clearly, account (9), Mpr":;; M;r" , but Mr Mp r" • p Hence Since so that, taking into Pm E F* (r ") M r" = M* r " • p p r "e r 1 ' we have In order to prove the opposite inequality, let V-y 1 E r 1 ' 1 ;;; there is an arc y" Y1 II E r" such that where p EF(r ) 1 Then, Hence J pds :;; J pds < 00.

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Analytic Functions Błażejewko 1982: Proceedings of a Conference held in Błażejewko, Poland, August 19–27, 1982 by Boris Nikolaevič Apanasov (auth.), Julian Ławrynowicz (eds.)


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