• Title, Summary, Keyword: integer translations

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Finitely normal families of integer translations

  • Kim, Jeong-Heon
    • Communications of the Korean Mathematical Society
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    • v.11 no.2
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    • pp.335-348
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    • 1996
  • For an open set G in the complex plane C, we prove the existence of an entire function f such that its integer translations forms a finitely normal family exactly on G if and only if G is periodic with period 1 and G has no hole.

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FRAMES BY INTEGER TRANSLATIONS

  • Kim, J.M.;Kwon, K.H.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.11 no.3
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    • pp.1-5
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    • 2007
  • We give an elementary proof of a necessary and sufficient condition for integer translates {${\phi}(t-{\alpha})\;:\;{\alpha}{\in}{\mathbb{Z}}^d$} of ${\phi}$(t) in $L^2({\mathbb{R}}^d)$ to be a frame sequence.

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Polynomials satisfying f(x-a)f(x)+c over finite fields

  • Park, Hong-Goo
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.2
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    • pp.277-283
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    • 1992
  • Let GF(q) be a finite field with q elements where q=p$^{n}$ for a prime number p and a positive integer n. Consider an arbitrary function .phi. from GF(q) into GF(q). By using the Largrange's Interpolation formula for the given function .phi., .phi. can be represented by a polynomial which is congruent (mod x$^{q}$ -x) to a unique polynomial over GF(q) with the degree < q. In [3], Wells characterized all polynomial over a finite field which commute with translations. Mullen [2] generalized the characterization to linear polynomials over the finite fields, i.e., he characterized all polynomials f(x) over GF(q) for which deg(f) < q and f(bx+a)=b.f(x) + a for fixed elements a and b of GF(q) with a.neq.0. From those papers, a natural question (though difficult to answer to ask is: what are the explicit form of f(x) with zero terms\ulcorner In this paper we obtain the exact form (together with zero terms) of a polynomial f(x) over GF(q) for which satisfies deg(f) < p$^{2}$ and (1) f(x+a)=f(x)+c for the fixed nonzero elements a and c in GF(q).

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