arXiv subjects

Bogdan Bojarski

Publications and source records attributed to Bogdan Bojarski.

4 recordsLinked to original sources

arXiv2012

Sobolev spaces and Lagrange interpolation

In this short paper the discussion of the pointwise characterization of functions $f$ in the Sobolev space $W^{m,p}(\R^n)$ given in the recent paper (Bojarski) is supplemented in \SS1 by a direct, essentially geometric, proof of the novel inequality (for $m>1$), appearing in Bojarski apparently for the first time, and involving the use of the $m$-th difference of the function $f$. Moreover in \SS2 some additional comments to the text in Bojarski are given and a natural class of Sobolev spaces in domains $G$ in $\R^n$ is defined. \SS3 contains some final remarks.

math.AP↗

arXiv2011

How to recognize polynomials in higher order Sobolev spaces

This paper extends characterizations of Sobolev spaces by Bourgain, Brézis, and Mironescu to the higher order case. As a byproduct, we obtain an integral condition for the Taylor remainder term, which implies that the function is a polynomial. Similar questions are also considered in the context of Whitney jets.

math.CA↗

arXiv2005

Correspondences and index

We define certain class of correspondences of polarized representations of $C^*$-algebras. Our correspondences are modeled on the spaces of boundary values of elliptic operators on bordisms joining two manifolds. In this setup we define the index. The main subject of the paper is the additivity of the index.

math.KT↗

arXiv2001

Generalized Riemann-Hilbert Transmission and Boundary Value Problems, Fredholm Pairs and Bordisms

We present classical and generalized Riemann-Hilbert problem in several contexts arising from $K$-theory and bordism theory. The language of Fredholm pairs turns out to be useful and unavoidable. We propose an abstract formulation of a notion of bordism in the context of Hilbert spaces equipped with splittings.

math.KT↗