A5012167174- Advanced Harmonic Analysis Research
- Spectral Theory in Mathematical Physics
- Geometry and complex manifolds
- Nonlinear Partial Differential Equations
- Geometric Analysis and Curvature Flows
- Mathematical Dynamics and Fractals
- Analytic Number Theory Research
- Advanced Mathematical Modeling in Engineering
- Mathematical Approximation and Integration
- Mathematical Analysis and Transform Methods
- European Socioeconomic and Political Studies
University of Georgia
2019-2024
University of Wisconsin–Madison
2020
We expand the class of curves $(φ_1(t),φ_2(t)),\ t\in[0,1]$ for which $\ell^2$ decoupling conjecture holds $2\leq p\leq 6$. Our includes all real-analytic regular with isolated points vanishing curvature and form $(t,t^{1+ν})$ $ν\in (0,\infty)$.
We expand the class of curves <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis phi 1 left-parenthesis t right-parenthesis comma 2 element-of left-bracket 0 right-bracket"> <mml:semantics> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>φ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mi>t</mml:mi> stretchy="false">)</mml:mo> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mtext> </mml:mtext>...
In this article, we study the problem of obtaining Lebesgue space inequalities for Fourier restriction operator associated to rectangular pieces paraboloid and perturbations thereof. We state a conjecture dependence norms in these on sidelengths rectangles, prove that follows from (a slight reformulation the) elliptic hypersurfaces, that, if valid, is essentially sharp. Such questions arise naturally degenerate hypersurfaces; demonstrate connection by using our positive results new class...
We find the precise range of $(p,q)$ for which local averages along graphs a class two-variable polynomials in $\mathbb{R}^3$ are restricted weak type $(p,q)$, given hypersurfaces have Euclidean surface measure. derive these results using non-oscillatory, geometric methods, model bearing strong connection to general real-analytic case.