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.
2020-01-01
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.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
10.1007_s00229-019-01167-0 (1).pdf
Solo gestori archivio
Tipologia:
Versione editoriale (Publisher’s layout)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
421.74 kB
Formato
Adobe PDF
|
421.74 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
