Edit Profile (opens in new tab) Zalik, Richard A. Compute Distance To: Compute Author ID: zalik.richard-a Published as: Zalik, R. A.; Zalik, Richard A. External Links: ORCID Documents Indexed: 67 Publications since 1975 Reviewing Activity: 283 Reviews Co-Authors: 13 Co-Authors with 25 Joint Publications 143 Co-Co-Authors all top 5 Co-Authors 41 single-authored 9 San Antolín, Angel 3 González, Alfredo Lázaro 2 Dikshit, Hanuman Prasad 2 Favier, Sergio J. 2 Kilgore, Theodore A. 2 Zwick, Daniel S. 1 Carnicer, Jésus Miguel 1 Chawla, Man M. 1 Olson, Timothy Edward 1 Passi, Kalpdrum 1 Peña, Juan Manuel 1 Saad, T. Abuabara 1 Vinogradov, Aleksandra M. all top 5 Serials 20 Journal of Approximation Theory 9 Journal of Mathematical Analysis and Applications 5 Proceedings of the American Mathematical Society 5 Applied and Computational Harmonic Analysis 3 Journal of Computational Analysis and Applications 2 The Journal of Fourier Analysis and Applications 2 Journal of Applied Functional Analysis 1 Computers & Mathematics with Applications 1 Applied Mathematics and Computation 1 Pacific Journal of Mathematics 1 Quarterly of Applied Mathematics 1 Transactions of the American Mathematical Society 1 Journal of Integral Equations and Applications 1 International Journal of Computer Mathematics 1 Advances in Computational Mathematics 1 Abstract and Applied Analysis 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Journal of Concrete and Applicable Mathematics all top 5 Fields 38 Approximations and expansions (41-XX) 29 Harmonic analysis on Euclidean spaces (42-XX) 9 Real functions (26-XX) 9 Functions of a complex variable (30-XX) 5 Numerical analysis (65-XX) 4 Functional analysis (46-XX) 2 Ordinary differential equations (34-XX) 2 Integral equations (45-XX) 1 History and biography (01-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral transforms, operational calculus (44-XX) 1 Operator theory (47-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 50 Publications have been cited 310 times in 203 Documents Cited by ▼ Year ▼ On the stability of frames and Riesz bases. Zbl 0829.46006Favier, S. J.; Zalik, R. A. 74 1995 Riesz bases and multiresolution analyses. Zbl 0944.42028Zalik, R. A. 15 1999 On transforming a Tchebycheff system into a complete Tchebycheff system. Zbl 0332.41019Zalik, R. A. 14 1977 Nonexistence of a Riesz basis of translates. Zbl 0764.42020Olson, Timothy Edward; Zalik, R. A. 13 1992 Existence of Tchebycheff extensions. Zbl 0303.41031Zalik, R. A. 12 1975 On approximation by shifts and a theorem of Wiener. Zbl 0403.41008Zalik, R. A. 11 1978 Inequalities for weighted polynomials. Zbl 0508.41012Zalik, R. A. 11 1983 Orthonormal wavelet systems and multiresolution analyses. Zbl 1198.42061Zalik, Richard A. 10 2010 Integral representation of Tchebycheff systems. Zbl 0377.41022Zalik, R. A. 9 1977 Strictly totally positive systems. Zbl 0903.41015Carnicer, J. M.; Peña, J. M.; Zalik, R. A. 8 1998 On MRA Riesz wavelets. Zbl 1136.42032Zalik, R. A. 7 2007 Matrix-valued wavelets and multiresolution analysis. Zbl 1262.42023San Antolín, Angel; Zalik, Richard A. 7 2012 Integral representation and embedding of weak Markov systems. Zbl 0688.41038Zalik, R. A. 7 1989 Some smooth compactly supported tight wavelet frames with vanishing moments. Zbl 1350.42056San Antolín, A.; Zalik, R. A. 7 2016 A characterization of Tchebycheff systems. Zbl 0383.41023Zalik, R. A. 6 1978 Smoothness properties of generalized convex functions. Zbl 0342.26008Zalik, R. A. 6 1976 On extending the domain of definition of Chebyshev and weak Chebyshev systems. Zbl 0684.41025Zalik, R. A.; Zwick, D. 6 1989 Weighted polynomial approximation on unbounded intervals. Zbl 0439.41008Zalik, R. A. 5 1980 The Müntz-Szasz theorem and the closure of translates. Zbl 0499.30009Zalik, R. A. 5 1981 Bases of translates and multiresolution analyses. Zbl 1141.42025Zalik, Richard A. 5 2008 Some weighted polynomial inequalities. Zbl 0533.41008Zalik, R. A. 5 1984 Remarks on a paper of Gel’fand and Shilov on Fourier transforms. Zbl 0552.30019Zalik, R. A. 5 1984 Erratum to “Embedding of weak Markov systems”. Zbl 0606.41047Zalik, R. A. 5 1985 Čebyšev and weak Čebyšev systems. Zbl 0890.41014Zalik, R. A. 5 1996 A family of nonseparable scaling functions and compactly supported tight framelets. Zbl 1306.42051San Antolín, A.; Zalik, R. A. 5 2013 Some bivariate smooth compactly supported tight framelets with three generators. Zbl 1276.42026San Antolín, A.; Zalik, R. A. 5 2013 The fundamentality of sequences of translates. Zbl 0479.42010Zalik, R. A. 4 1980 Some properties of Chebyshev systems. Zbl 1234.26068Zalik, Richard A. 4 2011 Some theorems concerning holomorphic Fourier transforms. Zbl 0639.42007Zalik, R. A.; Saad, T. Abuabara 4 1987 Approximation by nonfundamental sequences of translates. Zbl 0398.30019Zalik, R. A. 3 1980 Perturbations of the Haar wavelet. Zbl 0887.42022Govil, N. K.; Zalik, R. A. 3 1997 Integral representation of Markov systems and the existence of adjoined functions for Haar spaces. Zbl 0724.41031Zalik, R. A. 3 1991 Extension of periodic Tchebycheff systems. Zbl 0335.41014Zalik, R. A. 2 1976 Splicing of Markov and weak Markov systems. Zbl 0682.41048Kilgore, Theodore; Zalik, R. A. 2 1989 A recursive doubling algorithm for inverting tridiagonal matrices. Zbl 0724.65021Chawla, M. M.; Passi, K.; Zalik, R. A. 2 1990 Compactly supported Parseval framelets with symmetry associated to \(E_d^{(2)}(\mathbb{Z})\) matrices. Zbl 1428.42075San Antolín, A.; Zalik, R. A. 1 2018 On fundamental sequences of translates. Zbl 0434.42019Zalik, R. A. 1 1980 Relative differentiation, Descartes’ rule of signs, and the Budan-Fourier theorem for Markov systems. Zbl 0905.26008Zalik, R. A. 1 1998 Embedding of weak Markov systems. Zbl 0539.41039Zalik, R. A. 1 1984 A short proof that every weak Tchebycheff system may be transformed into a weak Markov system. Zbl 0744.41028Zalik, R. A. 1 1991 Representation of orthonormal multivariate wavelets. Zbl 1099.65156Zalik, R. A. 1 2006 Frames and Riesz bases: A short survey. Zbl 0912.42021Favier, S. J.; Zalik, R. A. 1 1997 A class of quasi-orthogonal wavelet bases. Zbl 0892.42021Zalik, Richard A. 1 1998 Riesz bases, multiresolution analyses, and perturbation. Zbl 1067.42025González, Alfredo L.; Zalik, Richard A. 1 2004 The Jeffcott equations in nonlinear rotordynamics. Zbl 0682.70022Zalik, R. A. 1 1989 A basis of weighted exponentials. Zbl 0694.46008Zalik, R. A. 1 1989 A new inequality for entire functions. Zbl 0698.30038Zalik, R. A. 1 1989 Some properties of Markov systems. Zbl 0727.41036Zalik, R. A.; Zwick, D. 1 1991 Erratum to: “Some smooth compactly supported tight wavelet frames with vanishing moments”. Zbl 1406.42038San Antolín, A.; Zalik, R. A. 1 2018 A family of nonseparable smooth compactly supported wavelets. Zbl 1271.42051San Antolín, A.; Zalik, R. A. 1 2013 Compactly supported Parseval framelets with symmetry associated to \(E_d^{(2)}(\mathbb{Z})\) matrices. Zbl 1428.42075San Antolín, A.; Zalik, R. A. 1 2018 Erratum to: “Some smooth compactly supported tight wavelet frames with vanishing moments”. Zbl 1406.42038San Antolín, A.; Zalik, R. A. 1 2018 Some smooth compactly supported tight wavelet frames with vanishing moments. Zbl 1350.42056San Antolín, A.; Zalik, R. A. 7 2016 A family of nonseparable scaling functions and compactly supported tight framelets. Zbl 1306.42051San Antolín, A.; Zalik, R. A. 5 2013 Some bivariate smooth compactly supported tight framelets with three generators. Zbl 1276.42026San Antolín, A.; Zalik, R. A. 5 2013 A family of nonseparable smooth compactly supported wavelets. Zbl 1271.42051San Antolín, A.; Zalik, R. A. 1 2013 Matrix-valued wavelets and multiresolution analysis. Zbl 1262.42023San Antolín, Angel; Zalik, Richard A. 7 2012 Some properties of Chebyshev systems. Zbl 1234.26068Zalik, Richard A. 4 2011 Orthonormal wavelet systems and multiresolution analyses. Zbl 1198.42061Zalik, Richard A. 10 2010 Bases of translates and multiresolution analyses. Zbl 1141.42025Zalik, Richard A. 5 2008 On MRA Riesz wavelets. Zbl 1136.42032Zalik, R. A. 7 2007 Representation of orthonormal multivariate wavelets. Zbl 1099.65156Zalik, R. A. 1 2006 Riesz bases, multiresolution analyses, and perturbation. Zbl 1067.42025González, Alfredo L.; Zalik, Richard A. 1 2004 Riesz bases and multiresolution analyses. Zbl 0944.42028Zalik, R. A. 15 1999 Strictly totally positive systems. Zbl 0903.41015Carnicer, J. M.; Peña, J. M.; Zalik, R. A. 8 1998 Relative differentiation, Descartes’ rule of signs, and the Budan-Fourier theorem for Markov systems. Zbl 0905.26008Zalik, R. A. 1 1998 A class of quasi-orthogonal wavelet bases. Zbl 0892.42021Zalik, Richard A. 1 1998 Perturbations of the Haar wavelet. Zbl 0887.42022Govil, N. K.; Zalik, R. A. 3 1997 Frames and Riesz bases: A short survey. Zbl 0912.42021Favier, S. J.; Zalik, R. A. 1 1997 Čebyšev and weak Čebyšev systems. Zbl 0890.41014Zalik, R. A. 5 1996 On the stability of frames and Riesz bases. Zbl 0829.46006Favier, S. J.; Zalik, R. A. 74 1995 Nonexistence of a Riesz basis of translates. Zbl 0764.42020Olson, Timothy Edward; Zalik, R. A. 13 1992 Integral representation of Markov systems and the existence of adjoined functions for Haar spaces. Zbl 0724.41031Zalik, R. A. 3 1991 A short proof that every weak Tchebycheff system may be transformed into a weak Markov system. Zbl 0744.41028Zalik, R. A. 1 1991 Some properties of Markov systems. Zbl 0727.41036Zalik, R. A.; Zwick, D. 1 1991 A recursive doubling algorithm for inverting tridiagonal matrices. Zbl 0724.65021Chawla, M. M.; Passi, K.; Zalik, R. A. 2 1990 Integral representation and embedding of weak Markov systems. Zbl 0688.41038Zalik, R. A. 7 1989 On extending the domain of definition of Chebyshev and weak Chebyshev systems. Zbl 0684.41025Zalik, R. A.; Zwick, D. 6 1989 Splicing of Markov and weak Markov systems. Zbl 0682.41048Kilgore, Theodore; Zalik, R. A. 2 1989 The Jeffcott equations in nonlinear rotordynamics. Zbl 0682.70022Zalik, R. A. 1 1989 A basis of weighted exponentials. Zbl 0694.46008Zalik, R. A. 1 1989 A new inequality for entire functions. Zbl 0698.30038Zalik, R. A. 1 1989 Some theorems concerning holomorphic Fourier transforms. Zbl 0639.42007Zalik, R. A.; Saad, T. Abuabara 4 1987 Erratum to “Embedding of weak Markov systems”. Zbl 0606.41047Zalik, R. A. 5 1985 Some weighted polynomial inequalities. Zbl 0533.41008Zalik, R. A. 5 1984 Remarks on a paper of Gel’fand and Shilov on Fourier transforms. Zbl 0552.30019Zalik, R. A. 5 1984 Embedding of weak Markov systems. Zbl 0539.41039Zalik, R. A. 1 1984 Inequalities for weighted polynomials. Zbl 0508.41012Zalik, R. A. 11 1983 The Müntz-Szasz theorem and the closure of translates. Zbl 0499.30009Zalik, R. A. 5 1981 Weighted polynomial approximation on unbounded intervals. Zbl 0439.41008Zalik, R. A. 5 1980 The fundamentality of sequences of translates. Zbl 0479.42010Zalik, R. A. 4 1980 Approximation by nonfundamental sequences of translates. Zbl 0398.30019Zalik, R. A. 3 1980 On fundamental sequences of translates. Zbl 0434.42019Zalik, R. A. 1 1980 On approximation by shifts and a theorem of Wiener. Zbl 0403.41008Zalik, R. A. 11 1978 A characterization of Tchebycheff systems. Zbl 0383.41023Zalik, R. A. 6 1978 On transforming a Tchebycheff system into a complete Tchebycheff system. Zbl 0332.41019Zalik, R. A. 14 1977 Integral representation of Tchebycheff systems. Zbl 0377.41022Zalik, R. A. 9 1977 Smoothness properties of generalized convex functions. Zbl 0342.26008Zalik, R. A. 6 1976 Extension of periodic Tchebycheff systems. Zbl 0335.41014Zalik, R. A. 2 1976 Existence of Tchebycheff extensions. Zbl 0303.41031Zalik, R. A. 12 1975 all cited Publications top 5 cited Publications all top 5 Cited by 220 Authors 34 Zalik, Richard A. 14 Vashisht, Lalit Kumar 11 Sun, Wenchang 10 Zhou, Xingwei 8 Christensen, Ole 6 San Antolín, Angel 5 Kaushik, Shiv Kumar 5 Malhotra, Hari Krishan 5 Zwick, Daniel S. 4 Peña, Juan Manuel 3 Atreas, Nikolaos D. 3 Bownik, Marcin 3 Filasová, Anna 3 Jain, Pawan Kumar 3 Kim, Hong Oh 3 Kim, Rae Young 3 Krokavec, Dusan 3 Lim, Jae Kun 3 Matusiak, Ewa 3 Stavropoulos, Theodoros 3 Zhu, Yucan 2 Aimar, Hugo A. 2 Aldroubi, Akram 2 Ascensi, Gerard 2 Deepshikha 2 Dörfler, Monika 2 Feichtinger, Hans Georg 2 Freeman, Daniel H. jun. 2 He, Xionghui 2 Heil, Christopher E. 2 Jindal, Divya 2 Kamyabi-Gol, Rajab Ali 2 Kilgore, Theodore A. 2 Kitahara, Kazuaki 2 Lubinsky, Doron S. 2 Lyubarskii, Yurii I. 2 Mohapatra, Ram Narayan 2 Nevai, Paul G. 2 Olevskii, Victor 2 Papadakis, Manos 2 Quesada, José María 2 Schlumprecht, Thomas 2 Sedletskiĭ, Anatoliĭ Mechislavovich 2 Shekhar, Chander 2 Sommer, Manfred 2 Torregrosa, Joan 2 Totik, Vilmos 2 Volkmer, Hans 2 Zhang, Jing 2 Zheng, Bentuo 1 Adcock, Ben 1 Almira, Jose María 1 Alyazidi-Asiry, Mansour 1 Amini, Massoud 1 Ansari, Khursheed Jamal 1 Baggett, Lawrence Wasson 1 Balan, Radu V. 1 Bauldry, William C. 1 Behera, Biswaranjan 1 Benedetto, John Joseph 1 Berasategui, Miguel 1 Bernardis, Ana L. 1 Bruna Floris, Joaquim 1 Bustamante González, Jorge 1 Cabrelli, Carlos A. 1 Carando, Daniel G. 1 Carnicer, Jésus Miguel 1 Carrizo, Ivana 1 Casazza, Peter George 1 Chawla, Man M. 1 Chen, Dongyang 1 Chen, Wenjian 1 Chen, Xiaoyan 1 Chen, Yan 1 Cheney, Elliott Ward jun. 1 Chistyakov, Gennadiy P. 1 Czaja, Wojciech 1 De Carli, Laura 1 Deng, Baiqiao 1 Diao, Chenzhe 1 Esmaeelzadeh, Fatemeh 1 Favier, Sergio J. 1 Faxen, Birger 1 Gandhi, Shelly 1 Ganzburg, Michael Iosifovich 1 Gasull, Armengol 1 Gataric, Milana 1 Golubov, Boris Ivanovich 1 Gómez-Cubillo, Fernando 1 Gopinath, B. 1 Gordillo, María Luisa 1 Gorosito, Osvaldo P. 1 Grohs, Philipp 1 Guo, Xunxiang 1 Gupta, Nisha 1 Han, Maoan 1 Hansen, Anders C. 1 Hasannasab, Marzieh 1 He, Jianxun 1 Heineken, Sigrid B. ...and 120 more Authors all top 5 Cited in 69 Serials 39 Journal of Approximation Theory 21 Applied and Computational Harmonic Analysis 20 Journal of Mathematical Analysis and Applications 11 Proceedings of the American Mathematical Society 11 International Journal of Wavelets, Multiresolution and Information Processing 8 The Journal of Fourier Analysis and Applications 4 Analysis Mathematica 3 Applicable Analysis 3 Applied Mathematics and Computation 3 Results in Mathematics 3 Acta Applicandae Mathematicae 3 Linear Algebra and its Applications 3 Acta Mathematica Sinica. English Series 3 Science China. Mathematics 2 Israel Journal of Mathematics 2 Mathematical Notes 2 Journal of Computational and Applied Mathematics 2 Mathematische Annalen 2 Transactions of the American Mathematical Society 2 Mathematical Problems in Engineering 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Banach Journal of Mathematical Analysis 2 Analysis and Mathematical Physics 2 Journal of Function Spaces 1 Bulletin of the Australian Mathematical Society 1 Journal of Mathematical Physics 1 Letters in Mathematical Physics 1 Rocky Mountain Journal of Mathematics 1 Arkiv för Matematik 1 Journal of Geometry and Physics 1 Canadian Mathematical Bulletin 1 Gaṇita 1 Integral Equations and Operator Theory 1 Journal of Differential Equations 1 The Journal of the Indian Mathematical Society. New Series 1 Mathematische Nachrichten 1 Memoirs of the American Mathematical Society 1 Numerical Functional Analysis and Optimization 1 Advances in Applied Mathematics 1 Zeitschrift für Analysis und ihre Anwendungen 1 Operations Research Letters 1 Acta Mathematica Hungarica 1 Bulletin of the Iranian Mathematical Society 1 Parallel Computing 1 Science in China. Series A 1 The Journal of Geometric Analysis 1 Aequationes Mathematicae 1 International Journal of Computer Mathematics 1 Journal of Nonlinear Science 1 The Journal of Analysis 1 Computational and Applied Mathematics 1 Bulletin des Sciences Mathématiques 1 Advances in Computational Mathematics 1 Integral Transforms and Special Functions 1 Mathematical Physics, Analysis and Geometry 1 Analysis in Theory and Applications 1 Mediterranean Journal of Mathematics 1 Journal of Mathematical Physics, Analysis, Geometry 1 Operators and Matrices 1 Asian-European Journal of Mathematics 1 Armenian Journal of Mathematics 1 Advances in Mathematical Physics 1 Advances in Pure and Applied Mathematics 1 Journal of Mathematical Extension 1 S\(\vec{\text{e}}\)MA Journal 1 Arabian Journal of Mathematics 1 International Journal of Applied and Computational Mathematics 1 Advances in Operator Theory 1 Bollettino dell’Unione Matematica Italiana all top 5 Cited in 23 Fields 130 Harmonic analysis on Euclidean spaces (42-XX) 69 Approximations and expansions (41-XX) 34 Functional analysis (46-XX) 17 Functions of a complex variable (30-XX) 12 Real functions (26-XX) 10 Operator theory (47-XX) 9 Numerical analysis (65-XX) 6 Ordinary differential equations (34-XX) 6 Abstract harmonic analysis (43-XX) 4 Systems theory; control (93-XX) 4 Information and communication theory, circuits (94-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Dynamical systems and ergodic theory (37-XX) 2 Computer science (68-XX) 1 Combinatorics (05-XX) 1 Special functions (33-XX) 1 Partial differential equations (35-XX) 1 Sequences, series, summability (40-XX) 1 General topology (54-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Operations research, mathematical programming (90-XX) Citations by Year