Geometric condition for universal interpolation in
Author:
William A. Squires
Journal:
Trans. Amer. Math. Soc. 280 (1983), 401413
MSC:
Primary 30E05; Secondary 30D15, 42A38
MathSciNet review:
712268
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Abstract: It is known that if is an entire function of exponential type and with for constants , independent of , then is a universal interpolation sequence. That is, given any sequence of complex numbers such that for constants independent of then there exists of exponential type such that . This note is concerned with finding geometric conditions which make a universal interpolation sequence for various spaces of entire functions. For the space of entire functions of exponential type a necessary and sufficient condition for to be a universal interpolation sequence is that , where is the number of points of in the disc of radius about , excluding , and are constants independent of . Results for the space are given but the theory is not as complete as for the above example.
 [BT]
Carlos
A. Berenstein and B.
A. Taylor, A new look at interpolation theory for entire functions
of one variable, Adv. in Math. 33 (1979), no. 2,
109–143. MR
544846 (80j:30053), http://dx.doi.org/10.1016/S00018708(79)80002X
 [E]
L.
Ehrenpreis, Solution of some problems of division. IV. Invertible
and elliptic operators, Amer. J. Math. 82 (1960),
522–588. MR 0119082
(22 #9848)
 [L]
A. F. Leont'ev, Representation of functions by generalized Dirichlet series, Math. U.S.S.R. Izv. 6 (1972), 12651277.
 [Le]
B.
Ja. Levin, Distribution of zeros of entire functions, American
Mathematical Society, Providence, R.I., 1964. MR 0156975
(28 #217)
 [S1]
W.
A. Squires, Necessary conditions for universal interpolation in
\cal𝐸′, Canad. J. Math. 33 (1981),
no. 6, 1356–1364. MR 645231
(83g:30040), http://dx.doi.org/10.4153/CJM19811049
 [S2]
, Ph.D. Thesis, University of Michigan, 1979.
 [BT]
 C. A. Berenstein and B. A. Taylor, A new look at interpolation theory for entire functions of one variable, Adv. in Math. 33 (1979), 109143. MR 544846 (80j:30053)
 [E]
 L. Ehrenpreis, Solutions of some problems of division. IV, Amer. J. Math. 57 (1960), 522588. MR 0119082 (22:9848)
 [L]
 A. F. Leont'ev, Representation of functions by generalized Dirichlet series, Math. U.S.S.R. Izv. 6 (1972), 12651277.
 [Le]
 B. Ja. Levin, Distribution of zeros of entire functions, Transl. Math. Monos., Vol. 5, Amer. Math. Soc., Providence, R.I., 1964. MR 0156975 (28:217)
 [S1]
 W. A. Squires, Necessary conditions for universal interpolation in , Canad. J. Math. 33 (1981), 13561364. MR 645231 (83g:30040)
 [S2]
 , Ph.D. Thesis, University of Michigan, 1979.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198307122687
PII:
S 00029947(1983)07122687
Article copyright:
© Copyright 1983
American Mathematical Society
