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Given a purely contractive matrix-valued analytic function $\Theta$ on the unit disc $\bm{D}$, we study the $\mc{U} (n)$-parameter family of unitary perturbations of the operator $Z_\Theta$ of multiplication by $z$ in the Hilbert space…
We provide a sufficient condition for an operator $T$ on a non-metrizable and sequentially separable topological vector space $X$ to be sequentially hypercyclic. This condition is applied to some particular examples, namely, a composition…
We consider the dynamical zeta functions of Selberg and Ruelle associated with the geodesic flow on a compact odd-dimensional hyperbolic manifold. These dynamical zeta functions are defined for a complex variable $s$ in some right-half…
FPSAC 2013 Extended Abstract. We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand…
In this short paper, we consider a quadruple $(\Omega, \AA, \theta, \mu)$,where $\AA$ is a $\sigma$-algebra of subsets of $\Omega$, and $\theta$ is a measurable bijection from $\Omega$ into itself that preserves the measure $\mu$. For each…
Ergodic Optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that "most" functions are optimized by measures supported on a periodic orbit, and it has…
Using orbifold techniques I construct the Schrodinger functional (SF) for a doublet of Wilson quarks with chirally rotated boundary conditions. This allows to perform checks of universality: for instance, the renormalized SF coupling…
Exact non-perturbative partition functions of coupling constants and external fields exhibit huge hidden symmetry, reflecting the possibility to change integration variables in the functional integral. In many cases this implies also some…
In this paper we develop the method of double operator integrals to prove trace formulae for functions of contractions, dissipative operators, unitary operators and self-adjoint operators. To establish the absolute continuity of spectral…
In the first part of this thesis, we present a general technique for establishing local and uniform continuity bounds for Schur concave functions. Our technique uses a particular relationship between majorization and the trace distance…
Using symmetric function theory, we study the cycle structure and increasing subsequence structure of permutations after various shuffling methods, emphasizing the role of Cauchy type identities and the Robinson-Schensted-Knuth…
This article presents a survey of recent developments on pseudodifferential operators on noncommutative tori. We describe currently available constructions of those operators: by means of a $C^*$--dynamical system, by using an analogue of…
We introduce a new basis of the non-commutative symmetric functions whose commutative images are Schur functions. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions…
Some new results about multidimensional Topological Persistence are presented, proving that the discontinuity points of a k-dimensional size function are necessarily related to the pseudocritical or special values of the associated…
This note deals with the boundedness of the $H^\infty$ functional calculus of Ritt operators $T$ and associated square function estimates. The purpose is to give a shorter, concise and slightly more general approach towards Le~Merdy's…
Determining if a symmetric function is Schur-positive is a prevalent and, in general, a notoriously difficult problem. In this paper we study the Schur-positivity of a family of symmetric functions. Given a partition \lambda, we denote by…
The eigenfunctions and eigenvalues of orbital angular momentum operator on noncommutative lattice for a circle poset by theta-quantization are constructed, and it is demonstrated that they are equivalent to those of the conventional quantum…
The purpose of this paper is to study the lower semicontinuity with respect to the strong $L^1$-convergence, of some integral functionals defined in the space SBD of special functions with bounded deformation. Precisely, let $U$ be a…
We investigate the shrinking target and recurrence set associated to non-autonomous measure-preserving systems on compact metric spaces, establishing zero-one criteria in the spirit of classical Borel-Cantelli results. Our first main…
There are few constructions of square-integrable automorphic functions on metaplectic groups. Such functions may be obtained by the residues of certain Eisenstein series on covers of groups, "theta functions," but the Fourier coefficients…