Abstract
In the present paper we introduce a mechanism for generation a new class of linear transformations that preserve real roots of polynomials by using the theory of variation diminishing kernel.
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Dhaouadi, L., Islem, I., Elmonser, H.: \(q\)-Macdonald function as a variation diminishing *\(q\)-kernel. J. Anal. 30, 1157–1177 (2022)
Dhaouadi, L.: On the \(q\)-Bessel Fourier transform. Bull. Math. Anal. Appl. 52, 42–60 (2013)
Fitouhi, A., Hamza, M., Bouzeffour, F.: The \(q\)-\(j_{\alpha }\) Bessel function. J. Approx. Theory 115, 144–166 (2002)
Fisk, S.: Polynomials, roots, and interlacing. arXiv:math/0612833v2
Forgacs, T., Piotrwsk, A.: Multiplier sequences for generalized Laguerre bases. Rocky Mt. J. Math. 43(4), 1141–1159 (2013)
Gasper, G., Rahman, M.: Basic hypergergeometric series, Encycopedia of mathematics and its applications. Cambridge University Press, Cambridge (1990)
Hirschman, I.I., Jr.: Variation diminishing Hankel transforms. J. Anal. Math. 8, 307–336 (1961)
Iserles, A., Norsett, S.P.: Zeros of transformed polynomials. Math. Anal. 2, 483–509 (1990)
Iserles, A., Saff, E.B.: Zeros of expansions in orthogonal polynomials. Math. Proc. Camb. Phil. Soc. 105, 559–573 (1989)
Jackson, F.H.: On a \(q\)-definite integrals. Q. J. Pure Appl. Math. 41, 193–203 (1910)
Koornwinder, T.H., Swarttouw, R.F.: On \(q\)-analogues of the Hankel and Fourier transforms. Trans. Am. Math. Soc. 333, 445–461 (1992)
Moak, D.: The \(q\)-analogue of the Laguerre polynomials. J. Math. Anal. Appl. 81, 20–47 (1981)
Trimèche, K.: Generalized Harmonic analysis and wavelet packets: an elementary treatment of theory and applications. CRC Press, Boca Raton (2001)
Swarttouw, RF.: The Hahn-Exton \(q\)-Bessel functions. In: PhD Thesis. Delft Technical University (1992)
Pólya, G., Schur, J.: Über zwei arten von factorenfolgen in der theorie der algebraischen gleichungen. Journal fur die reine und angewandtemathematik 144, 89–113 (1914)
Piotrowski, A.: Linear operators and the distribution of zeros of entire functions. In: Ph.D. Dissertation, University of Hawai‘i (2007)
Watson, G.N.: A Treatise on the theory of Bessel functions, 2nd edn. Cambridge University Press, Cambridge (1966)
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This work was supported by the DGRST research grant LR21ES10.
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Dhaouadi, L., Saidani, I. Linear transform that preserve real roots of polynomials. Anal.Math.Phys. 14, 65 (2024). https://doi.org/10.1007/s13324-024-00929-8
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DOI: https://doi.org/10.1007/s13324-024-00929-8
Keywords
- Linear transformations preserving real-rootedness
- Laguerre-Pólya class
- Zeros of polynomials
- Variation diminishing kernel.