Extrapolation of functions in the Denjoy class on a star-shaped compact set
Copyright policy )Extrapolation of functions in the Denjoy class on a star-shaped compact set
Functions \(f\) in Denjoy classes \({\mathcal D}^s(k)\) on compact subsets \(K\) of \(\mathbb{R}^n\) are approximated, uniformly with all derivatives, by polynomials \[ P_{f,m}(x)=\sum^m_{k=0}{1\over k!} \Biggl({m-1\over m}\Biggr)^k{d^k\over dt^k} f([-\log_m(1-t)]x|_{t=0}, \] where \(\log_m=\log(\log_{m-1})\), \(\log_1=\log\). Extensions with controlled \(\overline\partial\) derivative constructed by E. M. Dyn'kin are considered.
- Krasnoyarsk State University Russian Federation
- Krasnoyarsk State Medical University Russian Federation
Quasi-analytic and other classes of functions of one complex variable, \(C^\infty\)-functions, quasi-analytic functions, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), Denjoy classes
Quasi-analytic and other classes of functions of one complex variable, \(C^\infty\)-functions, quasi-analytic functions, Series expansions (e.g., Taylor, Lidstone series, but not Fourier series), Denjoy classes
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