Related papers: Differential operators on Schur and Schubert polyn…
This paper establishes existence of solutions for a partial differential equation in which a differential operator involving variable exponent growth conditions is present. This operator represents a generalization of the $p(\cdot)$-Laplace…
We associate a polynomial to any diagram of unit cells in the first quadrant of the plane using Kohnert's algorithm for moving cells down. In this way, for every weak composition one can choose a cell diagram with corresponding row-counts,…
We characterize geometric properties of Banach spaces in terms of boundedness of square functions associated to general Schrodinger operators of the form $L=-\Delta+V$, where the nonnegative potential $V$ satisfies a reverse Holder…
We introduce two new bases for polynomials that lift monomial and fundamental quasisymmetric functions to the full polynomial ring. By defining a new condition on pipe dreams, called quasi-Yamanouchi, we give a positive combinatorial rule…
We derive one-point functions of the loop operators of Hermitian matrix-chain models at finite $N$ in terms of differential operators acting on the partition functions. The differential operators are completely determined by recursion…
We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of…
In this paper we study some operators associated to the Rarita-Schwinger operators. They arise from the difference between the Dirac operator and the Rarita-Schwinger operators. These operators are called remaining operators. They are based…
We investigate the multidimensional Schrodinger operator L(q) with complex-valued periodic, with respect to a lattice, potential q when the Fourier coefficients of q with respect to the orthogonal system {exp(i(a,x))}, where a changes in…
In this paper, we investigate a series of W-type differential operators, which appear naturally in the symmetry algebras of KP and BKP hierarchies. In particular, they include all operators in the W-constraints for tau functions of higher…
We establish a ring isomorphism between the derived Hall algebra of the Jordan quiver and the ring of double symmetric functions (i.e., the ring of symmetric polynomials in two sets of countably many variables, invariant under the…
In this paper we investigate the one-dimensional Schrodinger operator L(q) with complex-valued periodic potential q when q\inL_{1}[0,1] and q_{n}=0 for n=0,-1,-2,..., where q_{n} are the Fourier coefficients of q with respect to the system…
The Verschiebung operators $\varphi_t $ are a family of endomorphisms on the ring of symmetric functions, one for each integer $t\geq2$. Their action on the Schur basis has its origins in work of Littlewood and Richardson, and is intimately…
We prove the bispectrality of some class of matrix Schr\"odinger operators with polynomial potentials that satisfy a second-order matrix autonomous differential equation. The physical equation is constructed using the formal theory of the…
A class of second order difference (discrete) operators with a partial algebraization of the spectrum is introduced. The eigenfuncions of the algebraized part of the spectrum are polinomials (discrete polinomials). Such difference operators…
The $(-1)$-Jacobi, Bannai-Ito, and $(-1)$-Meixner-Pollaczek polynomials are studied in [Trans. Amer. Math. Soc. 364 (2012), 5491-5507], [Adv. Math. 229 (2012), 2123-2158], and [Stud. Appl. Math. 153 (2024), e12728], respectively, through…
We show that a realization of the operator $L=|x|^\alpha\Delta +c|x|^{\alpha-1}\frac{x}{|x|}\cdot\nabla -b|x|^{\alpha-2}$ generates a semigroup in $L^p(\mathbb {R}^N)$ if and only if $D_c=b+(N-2+c)^2/4 > 0$ and…
In this paper we develop a potential theory for strongly degenerate parabolic operators of the form \[ \mathcal{L}:=\nabla_X\cdot(A(X,Y,t)\nabla_X)+X\cdot\nabla_{Y}-\partial_t, \] in unbounded domains of the form \[…
This paper deals with the approximation of a magnetic Schr\"odinger operator with a singular $\delta$-potential that is formally given by $(i \nabla + A)^2 + Q + \alpha \delta_\Sigma$ by Schr\"odinger operators with regular potentials in…
The higher step Grushin operators $\Delta_{\alpha}$ are a family of sub-elliptic operators which degenerate on a sub-manifold of $\mathbb{R}^{n+m}$. This paper establishes Carleman-type inequalities for these operators. It is achieved by…
One-dimensional Schr\"odinger operators with singular perturbed magnetic and electric potentials are considered. We study the strong resolvent convergence of two families of the operators with potentials shrinking to a point. Localized…