Related papers: NC functions over the nc Grassmannian

We show the existence of a natural Dirichlet-to-Neumann map on Riemannian manifolds with boundary and bounded geometry, such that the bottom of the Dirichlet spectrum is positive. This map regarded as a densely defined operator in the…

In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting…

A classical way to introduce tau functions for integrable hierarchies of solitonic equations is by means of the Sato-Segal-Wilson infinite-dimensional Grassmannian. Every point in the Grassmannian is naturally related to a Riemann-Hilbert…

We propose a method to extend submanifolds, singular Riemannian foliations and isometric actions from a boundary component of a noncompact symmetric space to the whole space. This extension method preserves minimal submanifolds,…

We obtain sharp estimates for a generalized Zalcman coefficient functional with a complex parameter for the Hurwitz class and the Noshiro-Warschawski class of univalent functions as well as for the closed convex hulls of the convex and…

For a Hermitian holomorphic vector bundle over a Hermitian manifold, we consider the Dolbeault Laplacian with $\overline\partial$-Neumann boundary conditions, which is a self-adjoint operator on the space of square-integrable differential…

Inspired by recent formul\ae\ of Dubrovin, Yang, and Zagier, we interpret the tau function enumerating stationary Gromov-Witten invariants of $\mathbb{P}^1$ as an isomonodromic tau function associated with a difference equation. As a…

We study a family of non-local isoperimetric energies $E_{\gamma,\varepsilon}$ on the round sphere $M = S^n$, where the non-local interaction kernel $K_\varepsilon$ is the fundamental solution of the Helmholtz operator $1 - \varepsilon^2…

We show how solutions to a large class of partial differential equations with nonlocal Riccati-type nonlinearities can be generated from the corresponding linearized equations, from arbitrary initial data. It is well known that evolutionary…

Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…

We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators representing operator roots of the transfer…

We study Riesz bases/Riesz sequences of reproducing kernels in the model space $K_\theta$ in connection with the corresponding Schur--Nevanlinna parameters and functions. In particular, we construct inner functions with given…

This paper is devoted to self-adjoint cyclically compact operators on Hilbert--Kaplansky module over a ring of bounded measurable functions. The spectral theorem for such a class of operators are given. We apply this result to partial…

We consider a space of infinitely smooth functions on an unbounded closed convex set in ${\mathbb R}^n$. It is shown that each function of this space can be extended to an entire function in ${\mathbb C}^n$ satisfying some prescribed growth…

Given the unital C$^*$-algebra $A$, the unitary orbit of the projector $p_0=\begin{pmatrix}1 & 0 \\ 0 & 0 \end{pmatrix}$ in the C$^*$-algebra $M_2(A)$ of $2\times 2$ matrices with coefficients in $A$ is called in this paper, the Riemann…

For $n\ge5$, it is well known that the moduli space $\mathfrak{M_{0,\:n}}$ of unordered $n$ points on the Riemann sphere is a quotient space of the Zariski open set $K_n$ of $\mathbb C^{n-3}$ by an $S_n$ action. The stabilizers of this…

We generalize the splitting theorem of Cai-Galloway for complete Riemannian manifolds with $\Ric\geq-(n-1)$ admitting a family of compact hypersurfaces tending to infinity with mean curvatures tending to $n-1$ sufficiently fast to the…

In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a bounded domain (with smooth boundary) in a given complete (not compact a priori) Riemannian manifold with Ricci bounded below . For this, we…

This article is devoted to the study of several algebras which are related to symmetric functions, and which admit linear bases labelled by various combinatorial objects: permutations (free quasi-symmetric functions), standard Young…

One of the basic objects in the Morse theory of circle-valued maps is Novikov complex - an analog of the Morse complex of Morse functions. Novikov complex is defined over the ring of Laurent power series with finite negative part. The main…