A note on a trigonometric moment problem
Author:
Robert M. Young
Journal:
Proc. Amer. Math. Soc. 49 (1975), 411415
MSC:
Primary 42A80
MathSciNet review:
0367548
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Abstract: A sequence is said to be an interpolating sequence for if the system of equations admits a solution in whenever . If the solution is unique then is said to be a complete interpolating sequence. It is shown that if the imaginary part of is uniformly bounded and if , then is a complete interpolating sequence and is a Schauder basis for . It is also shown that this result is sharp in the sense that the condition is not sufficient to guarantee that is an interpolating sequence.
 [1]
Ralph
Philip Boas Jr., Entire functions, Academic Press Inc., New
York, 1954. MR
0068627 (16,914f)
 [2]
R.
J. Duffin and A.
C. Schaeffer, A class of nonharmonic Fourier
series, Trans. Amer. Math. Soc. 72 (1952), 341–366. MR 0047179
(13,839a), http://dx.doi.org/10.1090/S00029947195200471796
 [3]
A.
E. Ingham, Some trigonometrical inequalities with applications to
the theory of series, Math. Z. 41 (1936), no. 1,
367–379. MR
1545625, http://dx.doi.org/10.1007/BF01180426
 [4]
M.
Ĭ. Kadec′, The exact value of the PaleyWiener
constant, Dokl. Akad. Nauk SSSR 155 (1964),
1253–1254 (Russian). MR 0162088
(28 #5289)
 [5]
Norman
Levinson, Gap and Density Theorems, American Mathematical
Society Colloquium Publications, v. 26, American Mathematical Society, New
York, 1940. MR
0003208 (2,180d)
 [6]
Raymond
E. A. C. Paley and Norbert
Wiener, Fourier transforms in the complex domain, American
Mathematical Society Colloquium Publications, vol. 19, American
Mathematical Society, Providence, RI, 1987. Reprint of the 1934 original.
MR
1451142 (98a:01023)
 [7]
Robert
M. Young, Interpolation in a classical Hilbert
space of entire functions, Trans. Amer. Math.
Soc. 192 (1974),
97–114. MR
0357823 (50 #10290), http://dx.doi.org/10.1090/S00029947197403578236
 [8]
Robert
M. Young, Inequalities for a perturbation
theorem of Paley and Wiener, Proc. Amer. Math.
Soc. 43 (1974),
320–322. MR 0340948
(49 #5698), http://dx.doi.org/10.1090/S00029939197403409484
 [1]
 R. P. Boas, Jr., Entire functions, Academic Press, New York, 1954. MR 16, 1914. MR 0068627 (16:914f)
 [2]
 R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341366. MR 13, 839. MR 0047179 (13:839a)
 [3]
 A. E. Ingham, Some trigonometrical inequalities with applications to the theory of series, Math. Z. 41 (1936), 367379. MR 1545625
 [4]
 M. I. Kadec, The exact value of the PaleyWiener constant, Dokl. Akad. Nauk SSSR 155 (1964), 12531254 = Soviet Math. Dokl. 5 (1964), 559561. MR 28 #5289. MR 0162088 (28:5289)
 [5]
 N. Levinson, Gap and density theorems, Amer. Math. Soc. Colloq. Publ., vol. 26, Amer. Math. Soc., Providence, R. I., 1940. MR 2, 180. MR 0003208 (2:180d)
 [6]
 N. Wiener and R. E. A. C. Paley, Fourier transforms in the complex domain, Amer. Math. Soc. Colloq. Publ., vol, 19, Amer. Math. Soc., Providence, R. I., 1934. MR 1451142 (98a:01023)
 [7]
 R. M. Young, Interpolation in a classical Hilbert space of entire functions, Trans. Amer. Math. Soc. 192 (1974), 97114. MR 0357823 (50:10290)
 [8]
 , Inequalities for a perturbation theorem of Paley and Wiener, Proc Amer. Math. Soc. 43 (1974), 320322. MR 0340948 (49:5698)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197503675485
PII:
S 00029939(1975)03675485
Keywords:
Interpolating sequence,
frames,
PaleyWiener space
Article copyright:
© Copyright 1975
American Mathematical Society
