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The work of Fricke-Klein [20] develops the deformation theory of hyperbolic structures on a surface Σ in terms of the space of representations of its fundamental group damental group π = π1(Σ) in SL(...
Let K/k be an extension of fields, and assume that it is primary: the algebraic closure of k in K is purely inseparable over k. The most interesting case in practice is when K/k is a regular ex...
Trace formula for the Sturm-Liouville eigenvalue problem with its applications to n-body problem.
Funar algebra $K_\infty=K_\infty(\alpha,\beta;k)$ is the quotient of the group algebra over a ring $k$ of the braid group $B_\infty$ by two cubic relations: $\sigma_1^3-\alpha\sigma_1^2+\beta\sigma_1-...
Koplienko gave a trace formula for perturbations of self-adjoint operators by operators of Hilbert-Schmidt class $\mathcal{B}_2(\mathcal{H})$. Recently Gesztesy, Pushnitski and Simon gave an alternati...
Let $\Phi:TM\to TM$ be a positive-semidefinite operator of class $C^1$ defined on a complete noncompact manifold $M$ isometrically immersed in a Hadamard space $\bar{M}$. In this paper, we given condi...
Abstract: We give criteria for products of Toeplitz and Hankel operators on the Fock (Segal-Bargmann) space to belong to the Dixmier class, and compute their Dixmier trace. At the same time, analogous...
Abstract: We consider the Schr{\"o}dinger operator $-\Delta +V(x)$ in $L^2({\bf R}^3)$ with a real short-range (integrable) potential $V$. Using the associated Fredholm determinant, we present new tra...
We study the spectral functional A 7→ Tr f(D + A) for a suitable function f, a self-adjoint operator D having compact resolvent, and a certain class of bounded self-adjoint operators A.
In this paper, we mainly study the derivation algebra of the free Lie algebra and the Chen Lie algebra generated by the abelianization H of a free group, and trace maps.
We propose a relative trace formula approach and state the corresponding fundamental lemma toward the global restriction problem involving Bessel or Fourier-Jacobi periods of unitary groups Un×Um, ex...
In this article, we discuss the Lefschetz trace formula for an adic space which is separated smooth of finite type but not necessarily proper over an algebraically closed non-archimedean field. Under...
In this paper we study the problem of minimizing the Sobolev trace Rayleigh quotient $\|u\|_{W^{1,p}(\Omega)}^p / \|u\|_{L^q(\partial\Omega)}^p$ among functions that vanish in a set contained on the b...
Using Effros-Handelman-Shen theorem and Elliott’s classification theorem of AF algebras, we show that there exists a unital simple AF algebra A with unique trace such that A K admits no trace scaling ...
We show that Caffarelli-Kohn-Nirenberg first order interpolation inequalities as well as weighted trace inequalities in Rn × R+ admit a better range of power weights if we restrict ourselves to the sp...

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