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We prove versions of the strong Szëgo limit theorem for certain classes of pseudodifferential operators defined on the Sierpiński gasket. Ourresults used in a fundamental way the existence of loc...
Boundedness results for multilinear pseudodifferential operators on products of modulation spaces are derived based on ordered integrability conditions on the short-time Fourier transform of the opera...
The numerical integration of many geometric partial di erential equations involves discrete approximations of several first- and second-order geometric di erential operators. In this paper, we consi...
Gradient, divergence and Laplace-Beltrami operators over surfaces have played im- portant roles in many 痚lds related to geometry and analysis, such as dirential ge- ometry, computational geometry a...
The numerical integration of many geometric partial dirential equations in- volve discrete approximations of some dirential geometric operators. In this paper, we consider consistent discretized a...
We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyse the arithmetic complexity of existing algorithms for LCLMs, as wel...
Abstract: An algebraic approach for factorizing nonlinear partial differential equations (PDEs) and systems of PDEs is provided. In the particular case of second order linear and nonlinear PDEs and ...
Abstract: In 1999, Grunbaum, Haine and Horozov defined a large family of commutative algebras of ordinary differential operators which have orthogonal polynomials as eigenfunctions. These polynomials ...
Abstract: In this paper we give enough conditions when the operator of the fourth order included in a commutative ring of ordinary differential operators of rank 2 is formally self-adjoint. In the cas...
Abstract: Let $\Phi$ be a concave function on $(0,\infty)$ of strictly lower type $p_{\Phi}\in(0,1]$ and $\omega\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$. We introduce the weighted local Orl...
Abstract: This paper is devoted to wavelet analysis on adele ring $\bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize finite-dimen...
Abstract: For two positive integers $m$ and $n$, we let ${\mathbb H}_n$ be the Siegel upper half plane of degree $n$ and let ${\mathbb C}^{(m,n)}$ be the set of all $m\times n$ complex matrices. In th...
Abstract: We give a natural generalization of the classification of commutative rings of ordinary differential operators, given in works of Krichever, Mumford, Mulase, and determine commutative rings ...
Let (a,m, l) be a Manin triple, and let M, L be algebraic groups with Lie algebras m, l respectively. We point out that the product L carries a natural structure of Poisson manifold,whose Poisson te...
We establish a correspondence between Young diagrams and differential operators of infinitely many variables. These operators form a commutative associative algebra isomorphic to the algebra of the co...

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