Results 21 to 30 of about 34 (33)
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
wiley +1 more source
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
wiley +1 more source
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
wiley +1 more source
Petrov-Galerkin method for small deflections in fourth-order beam equations in civil engineering
Nonlinear EngineeringThis study explores the Petrov–Galerkin method’s application in solving a linear fourth-order ordinary beam equation of the form u″″+qu=fu^{\prime\prime} ^{\prime\prime} +qu=f.
Youssri Youssri Hassan +3 more
doaj +1 more source
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
wiley +1 more source
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
wiley +1 more source
On Laguerre-Sobolev matrix orthogonal polynomials
Open MathematicsIn this manuscript, we study some algebraic and differential properties of matrix orthogonal polynomials with respect to the Laguerre-Sobolev right sesquilinear form defined by ⟨p,q⟩S≔∫0∞p*(x)WLA(x)q(x)dx+M∫0∞(p′(x))*W(x)q′(x)dx,{\langle p,q\rangle }_ ...
Fuentes Edinson +2 more
doaj +1 more source
Superelliptic Affine Lie algebras and orthogonal polynomials
Forum of Mathematics, SigmaWe construct two families of orthogonal polynomials associated with the universal central extensions of the superelliptic Lie algebras. These polynomials satisfy certain fourth-order linear differential equations, and one of the families is a particular ...
Felipe Albino dos Santos +2 more
doaj +1 more source
Spectra of Self-Similar Measures. [PDF]
Entropy (Basel), 2022 Cao YS, Deng QR, Li MT.
europepmc +1 more source