A5040141181- Advanced Harmonic Analysis Research
- Mathematical Approximation and Integration
- Analytic Number Theory Research
- Advanced Mathematical Modeling in Engineering
- Differential Equations and Boundary Problems
- Mathematical Analysis and Transform Methods
- Nonlinear Partial Differential Equations
- Mathematical functions and polynomials
- Numerical methods in inverse problems
- Point processes and geometric inequalities
- Holomorphic and Operator Theory
- Advanced Banach Space Theory
- Geometric Analysis and Curvature Flows
- Spectral Theory in Mathematical Physics
- advanced mathematical theories
- Advanced Mathematical Identities
- Analytic and geometric function theory
- Approximation Theory and Sequence Spaces
- Nonlinear Differential Equations Analysis
- Mathematical Inequalities and Applications
- Advanced Combinatorial Mathematics
- Advanced Mathematical Physics Problems
- Limits and Structures in Graph Theory
- Stability and Controllability of Differential Equations
- Advanced Topics in Algebra
University of Bergamo
2013-2024
University of Milano-Bicocca
2010-2020
Universidad de Navarra
2014
University of Insubria
2014
Indian Institute of Science Bangalore
2010
Politecnico di Milano
2005
University of Milan
1993-1999
University of Calabria
1999
We study the error in quadrature rules on a compact manifold.Our estimates are same spirit of Koksma-Hlawka inequality and they depend sort discrepancy sampling points generalized variation function.In particular, we give sharp quantitative for functions Sobolev classes.
In this work the authors deal with linear second order partial differential operators of following type $H=\partial_{t}-L=\partial_{t}-\sum_{i,j=1}^{q}a_{ij}(t,x) X_{i}X_{j}-\sum_{k=1}^{q}a_{k}(t,x)X_{k}-a_{0}(t,x)$ where $X_{1},X_{2},\ldots,X_{q}$ is a system real Hormander's vector fields in some bounded domain $\Omega\subseteq\mathbb{R}^{n}$, $A=\left\{ a_{ij}\left( t,x\right) \right\} _{i,j=1}^{q}$ symmetric uniformly positive definite matrix such that...
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X 1 comma upper 2 ellipsis Subscript q Baseline"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>X</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>…</mml:mo> <mml:mi>q</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">X_1,X_2,\ldots ,X_q</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a system of real...
() defined in some bounded domain and assume that the Xi satisfy Hörmander's rank condition of step r , . We extend to this nonsmooth context results which are well known for smooth vector fields, namely: basic properties distance induced by doubling condition, Chow's connectivity theorem, and, under stronger assumption Poincaré's inequality. By results, these facts also imply a Sobolev embedding. All tools allow us draw consequences about second order differential operators modeled on fields:
Abstract In this note we study estimates from below of the single radius spherical discrepancy in setting compact two-point homogeneous spaces. Namely, given a d -dimensional manifold $$\mathcal {M}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>M</mml:mi> </mml:math> endowed with distance $$\rho $$ <mml:mi>ρ</mml:mi> so that $$(\mathcal {M}, \rho )$$ <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>,</mml:mo> <mml:mo>)</mml:mo> </mml:mrow> is space and Riemannian measure $$\mu...
Let us consider the class of “nonvariational uniformly hypoelliptic operators”: Lu\equiv\sum_{i,j=1}^{q}a_{ij} (x) X_{i} X_{j} u where: X_1,X_2,\ldots,X_q is a system Hörmander vector fields in \mathbb{R}^{n} ( n>q ), \{a_{ij}\} q\times q elliptic matrix, and functions a_{ij} are continuous, with suitable control on modulus continuity. We prove that: \| \|_{BMO(\Omega^{\prime})} \leq c \left\{\left\|Lu\right\|_{BMO(\Omega)} + \left\| u\right\|_{BMO(\Omega)} \right\} for domains...
Let B be a convex body in \mathbb R^2 with piecewise smooth boundary and let \widehat {\chi}_B denote the Fourier transform of its characteristic function. In this paper we determine admissible decays spherical L^p -averages relate our analysis to problem geometry sets. As an application obtain sharp results on average number integer lattice points large bodies randomly positioned plane.
We prove a version of Rothschild-Stein's theorem lifting and approximation some related results in the context nonsmooth Hörmander's vector fields for which highest order commutators are only Hölder continuous.The theory explicitly covers case one field having weight two while others have one.
Abstract Revisiting and extending a recent result of M. Huxley, we estimate the L p ( $\mathbb{T}$ d ) Weak– norms discrepancy between volume number integer points in translated domains.