91¶ÌÊÓƵ

Ph.D. in Mathematics, 91¶ÌÊÓƵ of Virginia, (1989)

Research Interests

Functional Analysis, Prediction Theory

Articles

Cheng, R. and Felder, C. (2022). On the geometry of the multipliers on $\ell^p_A$. 9 , pp. 41-52.

Cheng, R. (2022). On the prediction of p-stationary processes. 85 , pp. 481-505.

Cheng, R., Ross, W. and Seco, D. (2022). Zeros of optimal polynomial approximants in $\ell^p_A$. 404.

Cheng, R. and Xu, Y. (2020). Minimum norm interpolation in the $\ell_1$ space. Analysis and Applications Special Issue on Mathematics of Data Science.

Cheng, R., Ross, W. T.. and Mashreghi, J. (2020). Inner vectors for Toeplitz operators. Complex Analysis and Spectral Theory.

Cheng, R. and Dragas, J. (2019). A Blaschke sequence that fails to be a zero set for $\ell^p_A$. Proceedings of the American Mathematical Society.

Cheng, R., Ross, W. T.. and Mashreghi, J. (2019). Inner functions and zero sets for $\ell^p_A$. Transactions of the American Mathematical Society.

Cheng, R. and Dragas, J. (2019). On the failure of canonical factorization in $\ell^p_A$. Journal of Mathematical Analysis and Its Applications 479 , pp. 1939-1955.

Cheng, R. (2018). Convergence of the best linear predictor of a stationary Gaussian random field. Journal of Fourier Analysis and Applications 24 , pp. 1-22.

Cheng, R., Mashreghi, J. and Ross, W. (2018). Optimal weak parallelogram constants for L^p. Mathematical Inequalities and Applications 21 , pp. 1047-1058.

Cheng, R., Ross, W. and Mashreghi, J. (2017). Birkhoff-James orthogonality and the zeros of an analytic function. Computational Methods and Function Theory 17 , pp. 499-523.

Cheng, R. (2017). An elementary approach to optimal discrete-time search strategies. Sequential Analysis 36 , pp. 541-552.

Cheng, R., Ross, W. and Mashreghi, J. (2017). Multipliers of sequence spaces. Concrete Operators, Special Issue 4 (1) , pp. 76-108.

Cheng, R. and Ross, W. T.. (2016). An inner-outer factorization in \ell^p with applications to ARMA processes. Journal of Mathematical Analysis and its Applications 437 , pp. 396-418.

Cheng, R. and Harris, C. (2015). Mixed norm spaces and prediction of SaS moving averages. Journal of Time Series Analysis 36 , pp. 853-875.

Cheng, R. (2015). Prediction of stationary random fields with incomplete quarterplane past. Journal of Multivariate Analysis 139 , pp. 245-258.

Cheng, R. and Ross, W. T.. (2015). Weak parallelogram laws on Banach spaces and applications to prediction. Periodica Mathematica Hungarica 71 , pp. 45-58.

Cheng, R. (2014). Sequential search beats two-parameter search. Sequential Analysis 33 , pp. 1-11.

Cheng, R., Seubert, S. M.. and Wiegmann, D. D.. (2014). Mate choice and the evolutionary stability of a fixed threshold in a sequential search strategy. Computational and Structural Biotechnology Journal 10 , pp. 8-11.

Cheng, R. and Harris, C. B.. (2013). Duality of the weak parallelogram laws on banach spaces. Journal of Mathematical Analysis and Its Applications 404 , pp. 64-70.

Cheng, R., Miamee, A. G.. and Pourahmadi, M. (2003). On the geometry of L^p(mu) with applications to infinite variance processes. Journal of the Australian Mathematical Society 74 , pp. 35-42.

Cheng, R., Miamee, A. G.. and Pourahmadi, M. (2000). Regularity and minimality of infinite variance processes. Journal of Theoretical Probability 13 , pp. 1115-1122.

Cheng, R. and Houdre, C. (1999). On the prediction of some Lp random fields. Journal of the Australian Mathematical Society 67 , pp. 31-50.

Cheng, R., Miamee, A. G.. and Pourahmadi, M. (1998). Some extremal problems in L^p(w). Proceedings of the American Mathematical Society 126 , pp. 2333-2340.

Cheng, R., Kinch, L. F.., Ebanks, B. R.., Larson, L. M.. and McFadden, R. B.. (1998). When does f^{-1} = 1/f?. American Mathematical Monthly 105 , pp. 704-717.

Cheng, R. and Klotz, L. Peter. (1997). Hardy spaces on products of halfplanes and prediction of homogeneous random fields. Zeitschrift fur Analysis und ihre Anwendungen 16 , pp. 519-542.

Cheng, R. and Pourahmadi, M. (1997). Prediction with incomplete past and interpolation of missing values. Statistics and Probability Letters 33 , pp. 341-346.

Cheng, R. (1997). Some Banach spaces of analytic functions and an extremal problem. Analysis Mathematica 23.

Cheng, R. (1995). Analytic range functions of several variables. Canadian Journal of Mathematics 41 , pp. 462-473.

Cheng, R. (1994). On the structure of shift-invariant subspaces of L^2(T^2,mu). Rocky Mountain Journal of Mathematics 24 , pp. 1307-1317.

Cheng, R. (1994). Outer factorization of operator valued weight functions on the torus. Studia Mathematica 110 , pp. 235-246.

Cheng, R. and Seubert, S. M.. (1994). Weakly outer polynomials. Michigan Mathematical Journal 41 , pp. 235-245.

Cheng, R. and Pourahmadi, M. (1993). Baxer's inequality and convergence of finite predictors for multivariate stationary processes. Probability Theory and Related Fields 95 , pp. 115-124.

Cheng, R. (1993). The mixing rate of a multivariate stationary process. Journal of Theoretical Probability 6 , pp. 603-617.

Cheng, R. (1993). The spectral measure of regular stationary random field with the weak or strong commutation property. Annals of Probability 21 , pp. 1263-1274.

Cheng, R. (1992). A strong mixing condition for second-order stationary random fields. Studia Mathematica 101 , pp. 139-153.

Cheng, R. (1992). Holder classes of vector valued functions and convergence of the best predictor. Journal of Multivariate Analysis 42 , pp. 110-129.

Cheng, R. (1992). On the prediction error for two-parameter stationary random fields. Bulletin of the Australian Mathematical Society 46 , pp. 167-175.

Cheng, R. (1992). On the rate of strong mixing in stationary Gaussian random fields. Studia Mathematica 101 , pp. 183-191.

Cheng, R. (1992). Rational spectral densities and strong mixing. Journal of Multivariate Analysis 42 , pp. 267-283.

Cheng, R. (1992). Weakly and strongly outer functions on the bidisc. Michigan Mathematical Journal 39 , pp. 99-109.

Cheng, R. and Trefil Jr., J. S.. (1985). Moving material into space without rockets. Physics Teacher 23 , pp. 85-90.

Books

Cheng, R., Mashreghi, J. and Ross, W. T.. (2020). Function Theory and $\ell^p$ Spaces. American Mathematical Society.

Cheng, R. (2007). Practical Chess Exercises: 600 Lessons from Tactics to Strategy. Wheatmark.

Book Chapters

Cheng, R., Ross, W. T.. and Mashreghi, J. (2019). Inner functions in reproducing kernel spaces Analysis of Operators on Function Spaces Birkhauser.

Conference Proceeding

Cheng, R. and Felder, C. (2022). On interpolation by functions in $\ell^p_A$ Proceedings of the AMS Special Session on Recent Progress in Function Theory and Operator Theory AMS.

Presentations

Cheng, R. (April 11, 2015). Introduction to Mathematical Typesetting with LaTeX Oral Presentation SIAM Math Awareness Conference Norfolk, Virginia.

Cheng, R. (January 23, 2015). Count It Twice! Keynote/Plenary Address Mu Alpha Theta Induction Ceremony Virginia Beach.