Related papers: A generalization of d'Alembert's functional equati…
If $\sigma$ is an automorphism of order $p$ of the semisimple group $\mathbf{G}$, there is a natural correspondence between mod $p$ cohomological automorphic forms on $\mathbf{G}$ and $\mathbf{G}^\sigma$. We describe this correspondence in…
Given a $\Gamma$-semigroup $S$, we construct a semigroup $\Sigma$ in such a way that one sided ideals and quasi-ideals of $S$ can be regarded as one sided ideals and quasi-ideals respectively of $\Sigma$. This correspondence and other…
Dickson's commutative semifields are an important class of finite division algebras. We generalise Dickson's construction of commutative division algebras by doubling both finite field extensions and central simple algebras and not…
The squared eigenfunctions of the spectral problem associated to the Camassa-Holm equation represent a complete basis of functions, which helps to describe the Inverse Scattering Transform for the Camassa-Holm hierarchy as a Generalised…
We construct a general algorithm generating the analytic eigenfunctions as well as eigenvalues of one-dimensional stationary Schroedinger Hamiltonians. Both exact and quasi-exact Hamiltonians enter our formalism but we focus on quasi-exact…
Let $A$ be a vector space of real valued functions on a non-empty set $X$ and $L:A\rightarrow\mathbb{R}$ a linear functional. Given a $\sigma$-algebra $\mathcal{A}$, of subsets of $X$, we present a necessary condition for $L$ to be…
Generalized eigenfunctions of the 3-dimensional relativistic Schr\"odinger operator $\sqrt{\Delta} + V(x)$ with $|V(x)|\le C < x >^{{-\sigma}}$, $\sigma > 1$, are considered. We show that the generalized eigenfunctions can be expressed as…
We propose (and prove under some restrictions) that the square class of the central value of the $L$-function of an everywhere unramified symplectic Galois representation is given by a universal cohomological formula. This phenomenon is…
In the present paper we deal with the following generalization of the sine-cosine equation \begin{equation*} \int f_1(x+y-t)+f_2(x-y+t) d\mu(t)=g(x)h(y) \end{equation*} for complex valued functions $f_1$, $f_2$, $g$ and $h$ defined on a…
Properties of the mappings \begin{align*} C&\mapsto\frac1{(2\pi i)^2}\int_{\Gamma_1}\int_{\Gamma_2}f(\lambda,\mu)\,R_{1,\,\lambda}\,C\, R_{2,\,\mu}\,d\mu\,d\lambda, C&\mapsto\frac1{2\pi i}\int_{\Gamma}g(\lambda)R_{1,\,\lambda}\,C\,…
In this paper, we calculate explicitly automorphism group of the Suzuki's Hopf algebra $A_{Nn}^{\mu\lambda}$ by viewing Yetter-Drinfeld modules as invariants of Hopf algebra automorphisms.
It is proved that the automorphism group of a semigroup being an inflation of its proper subsemigroup decomposes into a semidirect product of two groups one of which is a direct sum of full symmetric groups.
We describe the automorphism group of the endomorphism semigroup $\End(K[x_1,...,x_n])$ of ring $K[x_1,...,x_n]$ of polynomials over an {\it arbitrary} field $K$. A similar result is obtained for automorphism group of the category of…
We write a generating function for all spherical functions on the product of several copies of SU(2).
We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X. We also identify the…
The structure of a certain subgroup $S$ of the automorphism group of a partially commutative group (RAAG) $G$ is described in detail: namely the subgroup generated by inversions and elementary transvections. We define admissible subsets of…
We study derivatives of Schur and tau functions from the view point of the Abel-Jacobi map. We apply the results to establish several properties of derivatives of the sigma function of an (n,s) curve. As byproducts we have an expression of…
We construct the duality groups for N=2 Supersymmetric QCD with gauge group SU(2n+1) and N_f=4n+2 hypermultiplets in the fundamental representation. The groups are generated by two elements $S$ and $T$ that satisfy a relation…
We study the functional equation $A\circ X=X\circ B$, where $A,$ $B$, and $X$ are polynomials over $\mathbb C$. Using previous results of the author about polynomials sharing preimages of compact sets, we show that for given $B$ its…
Ranges of the real-valued parameters $\alpha$, $a$, $b$, and $m$ are identified for which the operator $$\mathcal{A}_{\alpha}(a,b)f(x):=x^\alpha\left(f''(x)+\frac{a}{x}f'(x)+\frac{b}{x^2}f(x)\right), \quad x>0,$$ generates an analytic…