RT Journal Article
T1 Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, II
A1 Rodríguez, José M.
A1 Romera, Elena
A1 Pestana, Domingo
A1 Álvarez, Venancio
AB ^aWe present a definition of general Sobolev spaces with respect to arbitrary measures, $W^{k,p}(\Omega,\mu)$ for $1\leq p\leq\infty$. In Part I [Acta Appl. Math. 80(3): 273-308 (2004), http://e-archivo.uc3m.es/handle/10016/6482] we proved that these spaces are complete under very mild conditions. Now we prove that if we consider certain general types of measures, then $C^\infty_c({\bf R})$ is dense in these spaces. As an application to Sobolev orthogonal polynomials, we study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.
PB Springer
SN 1000-9221 (Print)
SN 1573-8175 (Online)
YR 2002
FD 2002-06
LK https://hdl.handle.net/10016/6483
UL https://hdl.handle.net/10016/6483
LA eng
NO 32 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.-- Part I of this paper published in: Acta Appl. Math. 80(3): 273-308 (2004), available at: http://e-archivo.uc3m.es/handle/10016/6482
NO MR#: MR1928169 (2003h:42034)
NO Zbl#: Zbl 1095.42014
NO Research partially supported by a grant from DGES (MEC), Spain.
DS e-Archivo
RD 2 may. 2024