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Tractability of multivariate analytic problems
In the theory of tractability of multivariate problems one usually studies
problems with finite smoothness. Then we want to know which -variate
problems can be approximated to within by using, say,
polynomially many in and function values or arbitrary
linear functionals.
There is a recent stream of work for multivariate analytic problems for which
we want to answer the usual tractability questions with
replaced by . In this vein of research, multivariate
integration and approximation have been studied over Korobov spaces with
exponentially fast decaying Fourier coefficients. This is work of J. Dick, G.
Larcher, and the authors. There is a natural need to analyze more general
analytic problems defined over more general spaces and obtain tractability
results in terms of and .
The goal of this paper is to survey the existing results, present some new
results, and propose further questions for the study of tractability of
multivariate analytic questions
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