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Ph.D., Université de Montréal (1984) Office: Middlesex College, room 118 (click here for complete address) Tel: (1) 519-661-2111 ext 83639 E-mail: Area of research: Complex analysis, Approximation theory. |
My work is in complex analysis and approximation theory. The main research's theme is analytic approximation1.
1 "[ ...] the last term refers to the study of approximating capabilities of various classes of analytics functions on various sets and with respect to various metrics. Psychologically, the interest in such capabilities is of specific character; it is aroused by the desire "to spoil the good" (by making an analytic function reproduce, as accurately as possible, the behaviour of an "arbitrary function") rather than "to improve the bad" (by replacing, approximately, an "arbitrary" function with an analytic one)."My point of view is more qualitative than quantitative, in the sense that I am more interested to determine if it is possible to do the approximation than to find an efficient algorithm to compute this approximation. One of the practical consequences of qualitative approximation theory is of course that one should not waste time looking for an approximation that does not exist. The theoritical consequences are deep and important, providing a set of fundamental techniques which are used to simplify many arguments in mathematics2.
-- P. Sagué and V.P. Havin, St. Petersburg Math. J. 7 (1996).
2 "Mergelyan's [approximation] theorem (ingeniously applied) often provides a useful tool in the construction of analytic functions having prescribed boundary behaviour. [ ...] the powerful generalization of Mergelyan's theorem due to N. U. Arakelyan often applies directly to such situations, rendering ingenuity superfluous"I am especially interested in approximating a function by solutions of a system of differential equations. In particular, holomorphic functions, harmonic functions and other functions which are solutions of an elliptic partial differential equation have been considered and generalizations, with applications, of Arakelyan's theorem (see note 2 above) have been obtained.
-- L. Zalcman, Math. Reviews 46#2062 (1973).
Recently, I also have been interested by the theory of non-harmonic Fourier series, that is by the approximation properties of systems of exponentials { ei µn t }. The questions addressed (do they form a basis? do they form a frame?) have considerable contemporary importance in view of the connections with control theory and signal processing.
Telephone: (1) 519-661-2111 x 83639 (via switchboard)
Fax: (1) 519-661-3610
E-mail: 
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