On computing some extremal periodic positive-definite functions
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- Math. Comp. 27 (1973), 345-353 Request permission
Abstract:
This paper is concerned with maximizing the square integral over certain classes of periodic positive-definite functions. The question arose at Jet Propulsion Laboratory in connection with maximizing the average power of the received signal in radar exploration of the planets. We present computational evidence that the maximizing function exists and, in most but not all cases, is unique. Upper and lower bounds for the maximum square integral are computed, and formulas are conjectured for the maximizing functions in several cases.References
- Ralph Philip Boas Jr., Entire functions, Academic Press, Inc., New York, 1954. MR 0068627
- Sven Danø, Linear programming in industry. Theory and applications: An introduction, Springer-Verlag, Vienna, 1960. MR 0135620
- A. Garsia, E. Rodemich, and H. Rumsey, On some extremal positive definite functions, J. Math. Mech. 18 (1968/1969), 805–834. MR 0251454
- Wilhelm Magnus and Fritz Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin, 1943 (German). MR 0022272
- Norbert Wiener, The Fourier integral and certain of its applications, Dover Publications, Inc., New York, 1959. MR 0100201
- A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Math. Comp. 27 (1973), 345-353
- MSC: Primary 65K05
- DOI: https://doi.org/10.1090/S0025-5718-1973-0411168-7
- MathSciNet review: 0411168