Related papers: Quantitative Fredholm backstepping and rapid stabi…

Classical discrete-time adaptive controllers provide asymptotic stabilization and tracking; neither exponential stabilization nor a bounded noise gain is typically proven. In recent work it has been shown, in both the pole placement…

It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line {(with Dirichlet boundary conditions) is not essentially self-adjoint}: it has a continuous…

The index of a pseudo B-Fredholm operator will be defined and generalize the usual index of a B-Fredholm operator. This concept will be used to extend some known results in Fredholm's theory. Among other results, the nullity, the…

The existence, uniqueness, and exponential stability results for mild solutions to the fractional neutral stochastic differential system are presented in this article. To demonstrate the results, the concept of bounded integral contractors…

Suppose $\Gamma$ is a Carleson Jordan curve with logarithmic whirl points, $\varrho$ is a Khvedelidze weight, $p:\Gamma\to(1,\infty)$ is a continuous function satisfying $|p(\tau)-p(t)|\le -\mathrm{const}/\log|\tau-t|$ for $|\tau-t|\le…

For smooth hyperbolic dynamical systems and smooth weights, we relate Ruelle transfer operators with dynamical Fredholm determinants and dynamical zeta functions: First, we establish bounds for the essential spectral radii of the transfer…

We study idempotent, model, and Toeplitz operators that attain the norm. Notably, we prove that if $\mathcal{Q}$ is a backward shift invariant subspace of the Hardy space $H^2(\mathbb{D})$, then the model operator $S_{\mathcal{Q}}$ attains…

Regularization methods have been recently developed to construct stable approximate solutions to classical partial differential equations considered as final value problems. In this paper, we investigate the backward parabolic problem with…

We study jointly quasinormal and spherically quasinormal pairs of commuting operators on Hilbert space, as well as their powers. We first prove that, up to a constant multiple, the only jointly quasinormal $2$-variable weighted shift is the…

Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at…

Let $(X,d)$ be a uniformly locally finite metric space, and $T$ an operator in the uniform Roe algebra $C_u^*(X)$ (or uniform quasi-local algebra $C_{ql}^*(X)$). In this paper, we introduce the concept of limit operators of $T$ on galaxies…

Let T and S be two bounded linear operators from Banach spaces X into Y and suppose that T is Fredholm and the stability number k(T;S) is 0. Let d(T;S) be the supremum of all r > 0 such that dim N(T-\lambda S) and codim R(T-\lambda S) are…

In a previous work, we proved an index theorem for families of asymptotically hyperbolic discrete dynamical systems and obtained applications to bifurcation theory. A weaker and far more common assumption than asymptotic hyperbolicity is…

We introduce a numerical method to determine the stability of stationary pulse solutions of the complex Ginzburg-Landau equation. The method involves the computation of the point spectrum of the first-order linear differential operator with…

We present the current results in the study of weighted composition operators on weighted Banach spaces of an unbounded, locally finite metric space. Specifically, we determine characterizations of bounded and compact weighted composition…

We prove backward uniqueness for a class of ultraparabolic operators with coupled linear drift. The main difficulty is that the Fourier transform in the degenerate variables turns the coupled drift into a transport operator in the dual…

An analytic definition of a $\mathbb{Z}_2$-valued spectral flow for paths of real skew-adjoint Fredholm operators is given. It counts the parity of the number of changes in the orientation of the eigenfunctions at eigenvalue crossings…

The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…

Let $G$ be a compact Lie group acting smoothly on a smooth, compact manifold $M$, let $P \in \psi^m(M; E_0, E_1)$ be a $G$--invariant, classical pseudodifferential operator acting between sections of two vector bundles $E_i \to M$, $i =…

In this paper, we take the first step towards an extension of the nonlinear steepest descent method of Deift, Its and Zhou to the case of operator Riemann-Hilbert problems. In particular, we provide long range asymptotics for a Fredholm…