Related papers: The q-commuting contractions and $*$-regular dilat…
In this paper, we are interested to study the stability of the ascent of a mutually commuting n-tuple T submitted to a perturbation by an n-tuple S which commutes mutually with T. This study lead us to generalize some well known results for…
The explicit constructions of minimal isometric, and minimal unitary dilations of an arbitrary linear pencil of operators $T(\lambda)=T_0+\lambda T_1$ consisting of contractions on a separable Hilbert space for $|\lambda |=1$, which…
The objective of this paper is to study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. It is shown that, for a large class of analytic functional Hilbert spaces $\mathcal{H}_K$ on the unit ball in $\mathbb…
The summatory function of a $q$-regular sequence in the sense of Allouche and Shallit is analysed asymptotically. The result is a sum of periodic fluctuations for eigenvalues of absolute value larger than the joint spectral radius of the…
A noncommutative algebra of the complex $q$-twistors and their differentials is considered on the basis of the quantum $GL_q (4)\times SL_q (2)$ group. Real and pseudoreal $q$-twistors are discussed too. We consider the quantum-group…
The notion of $\tau$-tilting theory was introduced by Adachi, Iyama and Reiten at the beginning of the last decade and quickly became one of the most active areas of research in the representation theory of finite dimensional algebras. The…
We present a review of some recent models of gravitation theory with propagating torsion based on the use of a torsion-dilaton field and propose one more model of this type which promises to be more realistic. A proper universal…
We obtain intertwining dilation theorems for noncommutative regular domains D_f and noncommutative varieties V_J of n-tuples of operators, which generalize Sarason and Sz.-Nagy--Foias commutant lifting theorem for commuting contractions. We…
We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…
We use the theory of $x-y$ duality to propose a new definition / construction for the correlation differentials of topological recursion; we call it "generalized topological recursion". This new definition coincides with the original…
Using deformations inspired by relativistic considerations and phase space symmetry, we deform the position and momentum operators in one dimension. The resulting algebra is shown to yield the q-oscillator algebra in one limiting case and…
By studying the linearization of contour dynamics equation and using implicit function theorem, we prove the existence of co-rotating and travelling global solutions for the gSQG equation, which extends the result of Hmidi and Mateu…
One of the most important results in operator theory is And\^o's \cite{ando} generalization of dilation theory for a single contraction to a pair of commuting contractions acting on a Hilbert space. While there are two explicit…
We introduce Q-space, the tensor product of an index space with a primary space, to achieve a more general mathematical description of correlations in terms of q-tuples. Topics discussed include the decomposition of Q-space into a…
We appeal to a complex q-Fourier transform as a generalization of the (real) one analyzed in [Milan J. Math. {\bf 76} (2008) 307]. By recourse to tempered ultra-distributions we are able to show that the q-Gaussian distribution can be…
A technique to sum up the regular corrections appearing under the analytic continuation from the spacelike momentum region to the timelike one is proposed. A perturbative part of the inclusive semileptonic decay width of the tau-lepton in…
These are the notes of a lecture given at the university of Wroclaw in 1996. We present results of semigroups of (sub)positive contractions on L^p-spaces. The dilation theorem of Akcoglue and sucheston is considered as a starting point. We…
A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of…
By carrying out refined point-wise estimates for the mean curvature, we prove better rigidity theorems of Lagrangian and symplectic translating solitons.
By combining the Gessel--Xin method with plethystic substitutions, we obtain a recursion for a symmetric function generalization of the $q$-Dyson constant term identity also known as the Zeilberger--Bressoud $q$-Dyson theorem. This yields a…