Results 21 to 30 of about 56 (55)
On 2‐orthogonal polynomials of Laguerre type
International Journal of Mathematics and Mathematical Sciences, Volume 22, Issue 1, Page 29-48, 1999., 1999 Let be a sequence of 2‐orthogonal monic polynomials relative to linear functionals ω0 and ω1 (see Definition 1.1). Now, let be the sequence of polynomials defined by . When is, also, 2‐orthogonal, is called “classical” (in the sense of having the Hahn property). In this case, both and satisfy a third‐order recurrence relation (see below).
Khalfa Douak
wiley +1 more source
Fractal multiwavelets related to the cantor dyadic group
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 2, Page 307-314, 1998., 1997 Orthogonal wavelets on the Cantor dyadic group are identified with multiwavelets on the real line consisting of piecewise fractal functions. A tree algorithm for analysis using these wavelets is described. Multiwavelet systems with algorithms of similar structure include certain orthogonal compactly supported multiwavelets in the linear double‐knot ...
W. Christopher Lang
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Complex and distributional weights for sieved ultraspherical polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 2, Page 229-242, 1996., 1993 Contour integral and distributional orthogonality of sieved ultraspherical polynomials are established for values of the parameters outside the natural range of orthogonality by positive measures on the real line. A general representation theorem for moment functionals is included.
Jairo A. Charris, Felix H. Soriano
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On the distributional orthogonality of the general Pollaczek polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 3, Page 417-426, 1996., 1994 A distributional representation of the moment functional of the general Pollaczek polynomials is established. This representation holds for a wider range of parameters than the representation by a positive measure.
Jairo A. Charris, Felix H. Soriano
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Generating new classes of orthogonal polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 4, Page 643-656, 1996., 1994 Given a sequence of monic orthogonal polynomials (MOPS), {Pn}, with respect to a quasi‐definite linear functional u, we find necessary and sufficient conditions on the parameters an and bn for the sequence to be orthogonal. In particular, we can find explicitly the linear functional v such that the new sequence is the corresponding family of orthogonal
Amílcar Branquinho +1 more
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Some results on biorthogonal polynomials
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 625-636, 1994., 1993 Some biorthogonal polynomials of Hahn and Pastro are derived using a polynomial modification of the Lebesgue measure dθ combined with analytic continuation. A result is given for changing the measures of biorthogonal polynomials on the unit circle by the multiplication of their measures by certain Laurent polynomials.
Richard W. Ruedemann
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Finite‐infinite range inequalities in the complex plane
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 4, Page 625-638, 1991., 1991 Let E⫅C be closed, ω be a suitable weight function on E, σ be a positive Borel measure on E. We discuss the conditions on ω and σ which ensure the existence of a fixed compact subset K of E with the following property. For any p, 0 < P ≤ ∞, there exist positive constants c1, c2 depending only on E, ω, σ and p such that for every integer n ≥ 1 and every
H. N. Mhaskar
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A pair of biorthogonal polynomials for the Szegö‐Hermite weight function
International Journal of Mathematics and Mathematical Sciences, Volume 11, Issue 4, Page 763-767, 1988., 1987 A pair of polynomial sequences and where is of degree n in xk and is of degree m in x, is constructed. It is shown that this pair is biorthogonal with respect to the Szegö‐Hermite weight function |x|2μexp(−x2), (μ > −1/2) over the interval (−∞, ∞) in the sense that where m, n = 0, 1, 2, … and k is an odd positive integer.
N. K. Thakare, M. C. Madhekar
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Chebyshev systems and Sturm oscillation theory for discrete polynomials
Forum of Mathematics, SigmaWe prove an analogue of Chebyshev’s alternation theorem for linearly independent discrete functions $\Phi _n=\{\varphi _k\}_{k=1}^n$ on the interval $[0,q]_{\scriptscriptstyle \mathbb {Z}}=[0,q]\cap \mathbb {Z}$ . In particular, we establish
Dmitry Gorbachev +2 more
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Integer-valued polynomials satisfying growth constraints
Forum of Mathematics, SigmaWe consider polynomials which take integer values on the integers (IVPs), and satisfy an additional growth condition on the natural numbers. Elkies and Speyer, answering a question by Dimitrov, showed that there is a critical exponential growth threshold,
Avner Kiro, Alon Nishry
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