相关论文: Admissibility condition for exceptional Laguerre p…
This is a the first in a series of two articles devoted to the question of local solvability of doubly characteristic differential operators $L,$ defined, say, in an open set $\Om\subset \RR^n.$ Suppose the principal symbol $p_k$ of $L$…
We study the two-weighted estimate \[ \bigg\|\sum_{k=0}^na_k(x)\int_0^xt^kf(t)dt|L_{q,v}(0,\infty)\bigg\|\leq c\|f|L_{p,u}(0,\infty)\|,\tag{$*$} \] where the functions $a_k(x)$ are not assumed to be positive. It is shown that for $1<p\leq…
The aim of this paper is to bring into the picture a new phenomenon in the theory of orthogonal matrix polynomials satisfying second order differential equations. The last few years have witnessed some examples of a (fixed) family of…
In this paper we obtain new sufficient conditions for representation of a function as an absolutely convergent Fourier integral. Unlike those known earlier, these conditions are given in terms of belonging to weighted spaces. Adding weights…
In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of…
We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using…
We study the bispectrality of Laguerre type polynomials, which are defined by taking suitable linear combinations of a fixed number of consecutive Laguerre polynomials. These Laguerre type polynomials are eigenfunctions of higher-order…
For integers $a_0,a_1,\ldots,a_n$ with $|a_0a_n|=1$ and either $\alpha =u$ with $1\leq u \leq 50$ or $\alpha=u+ \frac{1}{2}$ with $1 \leq u \leq 45$, we prove that $\psi_n^{(\alpha)}(x;a_0,a_1,\cdots,a_n)$ is irreducible except for an…
In the work, the property of the second-order subdifferential is studied and second-order optimality conditions are obtained for the minimization problem. We also obtained necessary and sufficient conditions for an extremum for the extremal…
The basic purpose of the present paper is the full solutions of the inverse problem (i.e. a finding of necessary and sufficient conditions) for the operator with complex periodic coefficients.
The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Laguerre-Sobolev bilinear form with mass point at zero. In particular we construct the orthogonal polynomials using certain…
Let $V\in\mathbb{Q}(i)(\a_1,\dots,\a_n)(\q_1,\q_2)$ be a rationally parametrized planar homogeneous potential of homogeneity degree $k\neq -2, 0, 2$. We design an algorithm that computes polynomial \emph{necessary} conditions on the…
For the general second order linear differential operator $$\mathcal L_0 = \sum_{j, \, k=1}^n \, a_{jk} \, \partial_j \partial_k + \sum_{j=1}^n \, b_{j} \, \partial_j + c$$ with complex-valued distributional coefficients $a_{jk}$, $b_{j}$,…
In two recent papers necessary and sufficient conditions for a given system of second-order ordinary differential equations to be of Lagrangian form with additional dissipative forces were derived. We point out that these conditions are not…
Exactly solvable rationally-extended radial oscillator potentials, whose wavefunctions can be expressed in terms of Laguerre-type exceptional orthogonal polynomials, are constructed in the framework of $k$th-order supersymmetric quantum…
This paper is concerned with the polynomial integrability of the two-dimensional Hamiltonian systems associated to complex homogeneous polynomial potentials of degree $k$ of type $V_{k,l}=\alpha (q_2-i q_1)^l (q_2+iq_1)^{k-l}$ with…
We review recent results on superintegrable quantum systems in a two-dimensional Euclidean space with the following properties. They are integrable because they allow the separation of variables in Cartesian coordinates and hence allow a…
We present a number of identities involving standard and associated Laguerre polynomials. They include double-, and triple-lacunary, ordinary and exponential generating functions of certain classes of Laguerre polynomials.
We give a simpler proof of the a priori estimates obtained in the paper by Duran, Sanmartino and Toschi for solutions of elliptic problems in weighted Sobolev norms when the weights belong to the Muckenhoupt class $A_p$. The argument is a…
We use a recently found method to characterise all the invertible fourth-order difference equations linear in the extremal values based on the existence of a discrete Lagrangian. We also give some result on the integrability properties of…