We define and investigate the class τmN(x) of functions provided with the notion of m-approximate Nth degree Taylor polynomial at x∈ Rn. In particular we compare τmN(x) with the class tk,p(x) of functions having the derivative of order k in the Lp sense at x (Ziemer in Weakly differentiable functions. GTM, Springer, Berlin, 1989, Section 3.5). We apply this machinery to prove several properties of Sobolev functions, such as a new sectional superdensity property.

m-approximate Taylor polynomial / Delladio, S.. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 163:3-4(2020), pp. 481-505. [10.1007/s00229-019-01167-0]

m-approximate Taylor polynomial

Delladio S.
2020

Abstract

We define and investigate the class τmN(x) of functions provided with the notion of m-approximate Nth degree Taylor polynomial at x∈ Rn. In particular we compare τmN(x) with the class tk,p(x) of functions having the derivative of order k in the Lp sense at x (Ziemer in Weakly differentiable functions. GTM, Springer, Berlin, 1989, Section 3.5). We apply this machinery to prove several properties of Sobolev functions, such as a new sectional superdensity property.
3-4
Delladio, S.
m-approximate Taylor polynomial / Delladio, S.. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 163:3-4(2020), pp. 481-505. [10.1007/s00229-019-01167-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/295166
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