Related papers: Some non-algebraic forms of $\exp(A+B)$
Hecke operators on moduli of bundles over a global function field become substantially more complicated in the presence of ramification. We show that far enough in the Harder-Narasimhan cone of $\mathrm{Bun}_G$, this extra complexity has a…
We consider a rather general version of ladder operator $Z$ used by some authors in few recent papers, $[H_0,Z]=\lambda Z$ for some $\lambda\in\mathbb{R}$, $H_0=H_0^\dagger$, and we show that several interesting results can be deduced from…
We construct a class of representations of the quadratic R-matrix algebra, given by the reflection equation with the spectral parameter, in terms of certain ordinary difference operators. These operators turn out to act as parameter…
Factorization of quantum mechanical potentials has a long history extending back to the earliest days of the subject. In the present paper, the non-uniqueness of the factorization is exploited to derive new isospectral non-singular…
We extend the lattice-theoretic approach of Brandhorst--Cattaneo to classify algebraically trivial actions on the known IHS manifolds, up to deformation and birational conjugacy. In particular, we classify even order algebraically trivial…
For noncommutative variables x,y an expansion of log(exp(x)exp(y)) in powers of x+y is obtained.Each term of the series is given by an infinite sum in powers of x-y.The series is represented by diagrams.
Let A be a Hopf algebra and H a coalgebra. We shall describe and classify up to an isomorphism all Hopf algebras E that factorize through A and H: that is E is a Hopf algebra such that A is a Hopf subalgebra of E, H is a subcoalgebra in E…
For linear differential equations of the form $u'(t)=[A + B(t)] u(t)$, $t\geq0$, with a possibly unbounded operator $A$, we construct and deduce error bounds for two families of second-order exponential splittings. The role of quadratures…
We introduce the symmetric (respectively, non-symmetric) $\tau_{-\ell}-$hypergeometric functions associated with a root system of type $BC$ as joint eigenfunctions of a commutative algebra of differential (respectively,…
Let $E, F, E_0$ be Banach spaces, with $E_0$ a subspace of $E$. For a maximal Banach operator ideal $\mathcal{A}$, we show that a linear operator from $E_0$ to $F$ can be extended to a linear operator from $E$ to $F$ that belongs to…
We study the occurrence of factorization in polarized and unpolarized observables in coincidence quasi-elastic electron scattering. Starting with the relativistic distorted wave impulse approximation, we reformulate the effective momentum…
Considered is the equation $$ (T(a)+H(b))\phi=f, $$ where $T(a)$ and $H(b)$, $a,b\in L^\infty(\mathbb{T})$ are, respectively, Toeplitz and Hankel operators acting on the classical Hardy spaces $H^p(\mathbb{T})$, $1<p<\infty$. If the…
Let $B(H)$ be the algebra of bounded linear operators on a separable infinite-dimensional Hilbert space $H$. We study the commutant of $B(H)$ in its ultrapower. We characterize the class of non-principal ultrafilters for which this…
I briefly review some recent progress in the theory of nonleptonic B decays. After introducing the operator product expansion and the relevant effective Hamiltonian, I discuss the domain of validity and the theoretical justification of the…
We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank $N$. It combines and unifies the ideas of Duistermaat-Gr\"unbaum and Wilson. Our construction is completely…
Given a set $A$ and an abelian group $B$ with operators in $A$, in the sense of Krull and Noether, we introduce the Ore group extension $B[x; \sigma_B, \delta_B]$ as the additive group $B[x]$, with $A[x]$ as a set of operators. Here, the…
One-parameter generalizations of the logarithmic and exponential functions have been obtained as well as algebraic operators to retrieve extensivity. Analytical expressions for the successive applications of the sum or product operators on…
We summarize recent progress in the theory of exclusive rare and semileptonic B decays, focusing on model-independent results. The heavy-to-light form factors parameterizing these decays admit a model-independent description in two distinct…
We examine two classes of examples of Hausdorff \'etale factor groupoids; one comes from taking a quotient space of the unit space of an AF-groupoid, and the other comes from certain nonhomogeneous extensions of Cantor minimal systems…
The applicability of the factorization method is extended to the case of quantum fractional-differential Hamiltonians. In contrast with the conventional factorization, it is shown that the `factorization energy' is now a…