# On a coefficient in trace formulas for Wiener–Hopf operators

### Alexander V. Sobolev

University College London, UK

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## Abstract

Let $a = a(\xi), \xi \in \mathbb R,$ be a smooth function quickly decreasing at infinity. For the Wiener–Hopf operator $W(a)$ with the symbol $a$, and a smooth function $g\colon \mathbb C \to \mathbb C$, H. Widom in 1982 established the following trace formula:

where $\mathcal B(a; g)$ is given explicitly in terms of the functions $a$ and $g$. The paper analyses the coefficient $\mathcal B (a; g)$ for a class of non-smooth functions $g$ assuming that $a$ is real-valued. A representative example of one such function is $g(t) = |t|^{\gamma}$ with some $\gamma \in (0, 1]$.

## Cite this article

Alexander V. Sobolev, On a coefficient in trace formulas for Wiener–Hopf operators. J. Spectr. Theory 6 (2016), no. 4 pp. 1021–1045

DOI 10.4171/JST/151