Uniform bounds on biorthogonal functions for real exponentials with an application to the control theory of parabolic equations
Hector O. Fattorini, David L. Russell · Quarterly of Applied Mathematics · 1974
Abstract : In the report the authors study harmonic properties of sequences (e - (lambda sub k)t) of real exponential functions. Linear independence results, including estimates on the norms of biorthogonal functions, are obtained in the space (L sup 2) over the interval = or > 0, but 0. The results are uniform in that they depend only upon certain separation requirements on the (lambda sub k) rather than upon the individual sequence (lambda sub k). The results are used to study the boundary value controllability of the heat equation in the unit ball of (R sup n). (Author)