Uniform Bounds on Biorthogonal Functions for Real Exponentials with an Application to the Control Theory of Parabolic Equations.
Technical rept. 1 Oct 72-30 Sep 73,
WISCONSIN UNIV MADISON DEPT OF MATHEMATICS
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In the report the authors study harmonic properties of sequences e - lambda sub kt 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 infinity and in L sup 20,T, T 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
- Theoretical Mathematics