Richard A. ZalikProfessor |

- Applied Harmonic Analysis
- Applied Mathematics
- Approximation Theory

- Existence of Tchebycheff extensions, J. Mathematical Analysis and Applications 51 (1975), 68--75.
- Smoothness properties of generalized convex functions, Proceedings of the American Mathematical Society 56 (1976), 118--120.
- Extension of periodic Tchebycheff systems, J. Mathematical Analysis and Applications 56 (1976), 373--378.
- On transforming a Tchebycheff system into a complete Tchebycheff system, J. Approximation Theory 20 (1977), 220--222.
- A characterization of Tchebycheff systems, J. Approximation Theory 22 (1978), 356--359.
- Functions of bounded variation with respect to a Tchebycheff system, J. Approximation Theory 23 (1978), 318--323.
- On Approximation by shifts and a theorem of Wiener, Transactions of the American Mathematical Society, 243 (1978), 299--308.
- Approximation by nonfundamental sequences of translates, Proceedings of the American Mathematical Society, 78 (1980), 261--266.
- On fundamental sequences of translates, Proceedings of the American Mathematical Society 79 (1980), 255--259.
- Weighted Polynomial Approximation on Unbounded Intervals, J. Approximation Theory 28 (1980), 113--119.
- The fundamentality of sequences of translates, in E. W. Cheney (editor), Approximation Theory III, Academic Press, New York (1980), 927--932.
- The Müntz--Szász theorem and the closure of translates, J. Mathematical Analysis and Applications 82 (1981), 361--369.
- Inequalities for weighted polynomials, J. Approximation Theory 37 (1983), 137--146.
- Some properties of sequences of weighted exponentials, in Chui, Schumaker and Ward (editors), Approximation Theory IV, Academic Press, New York (1983), 729--732.
- Remarks on a paper of Gel'fand and Šilov on Fourier Transforms, J. Mathematical Analysis and Applications 102 (1984), 102--112.
- Some weighted polynomial inequalities, J. Approximation Theory 41 (1984), 39--50.
- Embedding of weak Markov systems, J. Approximation Theory 41 (1984), 253--256.
- Nonlinear Rotordynamics Analysis. Contract NAS8--36475 NASA Marshall Space Flight Center, 1986 (with William B. Day) (reviewed in NASA Tech Briefs 12 No. 7 (1988), 75.)
- Some theorems concerning holomorphic Fourier transforms (with T. Abuabara Saad), J. Mathematical Analysis and Applications 126 (1987), 483--493.
- Embedding a function into a Haar space, J. Approximation Theory 55 (1988), 61--64.
- Rotordynamic Analysis of a Bearing Tester, in Research Reports--1988 NASA/ASEE Summer Faculty Fellowship Program, NASA CR--183553.
- On the nonlinear Jeffcott equations, in IMACS Transactions on Scientific Computing, 12th. IMACS World Congress, Paris 1988, Vol. 1 (W. F. Ames et al., eds.,), 39--42. J. C. Baltzer, Basel, 1989.
- On extending the domain of definition of Čebyšev and weak Čebyšev systems (with D. Zwick), J. Approximation Theory 57 (1989), 202--210.
- Integral representation and embedding of weak Markov system, J. Approximation Theory 58 (1989), 1--11.
- A basis of weighted exponentials, J. Mathematical Analysis and Applications 141 (1989), 291--301.
- The Jeffcott equations in nonlinear rotordynamics, Quarterly of Applied Mathematics 47 (1989), 585--599.
- Determination of stability margins for a simple Jeffcott model, in Proceedings of the International Congress on Recent Developments in Air and Structure Borne Sound and Vibration (M. Crocker, ed.), 881--886, Auburn University, 1990.
- Extensions of endpoint equivalent and periodic Tchebycheff systems (with T. A. Kilgore), J. Approximation Theory 61 (1990), 360--370.
- A short proof that every weak Tchebycheff system may be transformed into a weak Markov system, J. Approximation Theory 64 (1991), 119--121.
- Integral representation of Markov systems and the existence of adjoined functions for Haar spaces, J. Approximation Theory 65 (1991), 22--31.
- Some properties of Markov systems (with D. Zwick), J. Approximation Theory 65 (1991), 32--45.
- Nondegeneracy and integral representation of weak Markov systems, J. Approximation Theory 68 (1992), 25--32.
- Nonexistence of a Riesz Basis of Translates (with T. E. Olson), in Approximation Theory (G. A. Anastassiou, Ed.), 401--408, Marcel Dekker, New York, 1992.
- The quasi--elastic method of solution for a class of integrodifferential equations (with A. M. Vinogradov), J. Integral Equations and Applications 5 (1993), 277--295.
- Quasiconformality and quasiregularity of Wachspress type rational complex planar splines of degree (3,1) (with H. P. Dikshit and A. Ojha), Advances in Computational Mathematics 2 (1994), 235--250.
- Rational complex planar splines (with H. P. Dikshit and A. Ojha), in Proceedings of the Conference on Advances in Computational Mathematics: New Delhi, India (H. P. Dikshit and C. A. Micchelli, Eds.), 235--242, World Scientific, Singapore, 1994.
- On the stability of frames and Riesz bases (with S. J. Favier), Appl. Comput. Harm. Analysis 2 (1995), 160--173. Postcript file Pdf file
- Some remarks on spectral approximation, Computers Math. Applic. 30 (1995), 235--241.
- Čebyšev and Weak Čebyšev systems, in Total Positivity and its Applications (M. Gasca and C. A. Micchelli, Eds.), 301--332, Kluwer Academic Publishers, Dordrecht, 1996.
- Tribute to Oved Shisha (with D. S. Lubinsky), J. Approximation Theory 86 (1996), 1--12.
- Frames and Riesz Bases: A Short Survey (with S. J. Favier), in Wavelet Theory and Harmonic Analysis in Applied Sciences (E. M. Fernández-Berdaguer and C. E. D'Atellis, Eds.), 93--114, Birkhäuser, Boston, 1997.
- Perturbations of the Haar Wavelet (with N. K. Govil), Proc. Amer. Math. Soc. 125 (1997), 3363--3370. Postcript file Pdf file
- Frames and Riesz bases (with S. J. Favier), in Fourier Analysis, Approximation Theory and Applications (Z. U. Ahmad, N. K. Govil and P. K. Jain, Eds.), 59--76, New Age International, New Delhi, 1997.
- A Class of Quasi--orthogonal Wavelet Bases, in Wavelets, Multiwavelets and their Applications (A. Aldroubi and E. B. Lin, Eds.), 81--94, Contemporary Mathematics, Vol. 216, American Mathematical Society, Providence, RI, 1998.
- Strictly totally positive systems (with J. M. Carnicer and J. M. Peña), J. Approximation Theory 92 (1998), 411--441. Postcript file Pdf file
- Interpolation, the Budan-Fourier theorem, and Descartes' rule of signs for Markov systems, in Approximation Theory: In Memory of A.K. Varma, (N.K. Govil, R.N. Mohapatra, Z. Nashed, A. Sharma and J. Szábados, Eds.), Marcel Dekker, New York, 1998, pp. 499--511.
- Riesz Bases and Multiresolution Analyses, Appl. Comput. Harm. Analysis 7 (1999), 315--331.
- Density and Approximation Properties of Markov Systems (with A. L. González), J. Computational Analysis and Applications 2 (2000), 49--87. Postcript file Pdf file
- On affine Riesz wavelets, in Algorithms for Approximations IV, Proceedings of the International Symposium held in 2001. (J. Levesley, I. J. Anderson and J. C. Mason, Eds.). University of Huddersfield, UK, (2002), pp. 362--369 (with A. L. González).
- Riesz bases, multiresolution analyses, and perturbation (with A. L. González) in Wavelets, Frames, and Operator Theory (D. Larson, P. E. T. Jorgensen and C. Heil, Eds.), 163--182. Contemporary Mathematics, Vol. 345, American Mathematical Society, Providence, RI, 2004. Postcript file Pdf file
- Density and Approximation Properties of weak Markov Systems (with A. L. González), J. Computational Analysis and Applications 6 (2004), 5-18. Postcript file Pdf file
- Representation of Orthonormal Multivariate Wavelets, in ``Splines and Wavelets: Athens 2005" (G. Chen and M--J. Lai, Eds.), pp. 507--515, Nashboro Press, Brentwood, TN 2005. Postcript file Pdf file
- On MRA Riesz wavelets, Proc. American Math. Soc. 135 (2007), 777-785. Postcript file Pdf file
- Bases of translates and multiresolution analyses, Applied and Computational Harmonic Analysis 24 (2008), 41-57. Postcript file Pdf file Corrigendum, Applied and Computational Harmonic Analysis 29 (2010), 121. Postcript file. Pdf file
- Orthonormal wavelet systems and multiresolution analyses, J. Appl. Functional Analysis 5 (2010), 31-41. Postcript file Pdf file
- Some properties of Chebyshev systems, J. Computational Analysis and Applications 13 (2011), 20-26. Pdf file
- Matrix-valued wavelets and multiresolution analysis (with A. San Antolín), J. Applied Functional Analysis 7 (2012), 13--25. Pdf file
- The method of Laplace and Watson's lemma, J. Concrete and Applicable Math. 10 (2012), 11--16. Pdf file
- Some smooth compactly supported tight framelets (with A. San Antolín), Communications in Mathematics and Applications 3 (2012), 345-353. Pdf file
- A family of nonseparable smooth compactly supported wavelets (with A. San Antolín), International Journal of Wavelets, Multiresolution and Information Processing 11, No.2 (2013).\\ DOI: 10.1142/S0219691313500148. Pdf file
- A family of nonseparable scaling functions and compactly supported tight framelets (with A. San Antolín), J. Mathematical Analysis and Applications 404 (2013), 201-211. DOI: 10.1016/j.jmaa.2013.02.040. Pdf file
- Some bivariate smooth compactly supported framelets with three generators (with A. San Antolín), Abstract and Applied Analysis, vol 2013, Article ID 818907, 7 pages, 2013. doi:10.1155/2013/818907. Pdf file
- Some smooth compactly supported tight wavelet frames with vanishing moments (with A. San Antolín), to appear in J. Fourier Analysis and Applications. Pdf file
- Some smooth compactly supported tight framelets associated to the quincux matrix (with A. San Antolín), to appear in J. Mathematical Analysis and Applications. Pdf file
- Tight framelets with smooth compactly supported generators,
(with A. San Antolín), preprint.
Pdf file
Richard A. Zalik

221 Parker Hall

Department of Mathematics and Statistics

Auburn University, Alabama 36849-5310

Email:zalik@auburn.edu