Browsing by Subject "Interpolation"
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Item An extension of Young's inequality(Texas Tech University, 1988-08) Sissel, Charles DennisNot availableItem Automatic generation of shape preserving quadratic splines(Texas Tech University, 1985-12) Hsu, Kim TNot availableItem Controlling zeros of interpolating series(Texas Tech University, 2001-05) Robinson, Jeffrey N.Some interesting problems arise when classical complex analysis techniques are applied to digital filter theory. Polynomials used in the interpolation of digital signals are called interpolating polynomials. These pol5momials may require modification to assure the convergence of their reciprocals on the unit circle. Such modifications were a principal concern of an earlier paper by R. Barnard, W. Ford and Y. Wang [4]. The distribution of zeros and the orthogonality property of {sinc(m>2:)} enables the construction of an infinite interpolating series for digital signals to which classical results can be applied [4]. For practical purposes it is convenient to consider finite truncations of the infinite series PN- A property that was observed in [4] was that the polynomials obtained by truncating the interpolating series P^ had the property that all of their zeros lie on the unit circle. Natural generalizations of the sine functions are the Bessel functions, Gegenbauer and Jacobi polynomials, and polynomials generated by certain measures. In this paper, we consider polynomials which are obtained by truncating infinite series which are generalizations of the interpolating series P^. We show that these polynomials do not have the property that their zeros lie on the unit circle when the infinite series is based on one of the above natural generalizations of the sine functions.Item Interpolation and approximation in the space of Dirichlet polynomials(Texas Tech University, 1989-05) Brown, James FNot availableItem On Edgeworth expansions with unknown cumulants(Texas Tech University, 1972-08) Coberly, William ArthurNot availableItem Tangential and osculatory interpolation(Texas Tech University, 1936-05) Schwalbe, Cecil ONot availableItem The mathematics of interpolation and sampling(Texas Tech University, 1986-08) Smith, Jennifer KIn this thesis, continuous time, autonomous, observable dynamical systems are studied. The main problem considered is whether sampling at discrete times preserves observability. The discrete observability problem is shown to be equivalent to the general theory of linear interpolation. The mathematical theory used in this paper is Polya's property W which is used to produce several new results. In addition, the problem of discrete sampling is also interpreted as an n-point boundary value problem and as a problem of independence in the dual space.