Computer assisted
Fourier analysis in sequence spaces of varying
regularity
Jean-Philippe
Lessard and Jason D. Mireles James
This work treats a
functional analytic framework for computer assisted
Fourier analysis which can be used to obtain
mathematically rigorous error bounds on numerical
approximations of solutions of differential equations.
An abstract a-posteriori theorem is employed in order to
obtain existence and regularity results for
problems with
or
.
The main tools are certain infinite sequence spaces of
rapidly decaying coefficients: we employ sequence spaces
of algebraic and exponential decay rates in order to
characterize the regularity our results. We illustrate
the implementation and effectiveness of the method in a
variety of regularity classes. We also examine the
effectiveness of spaces of algebraic decays for studying
solutions of problems near the breakdown of analyticity.
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