The singular values of the logarithmic potential transform on bound states spaces of Landau Hamiltonian

Landau singularities and singularities of holonomic integrals of the Ising class

We consider families of multiple and simple integrals of the ``Ising class'' and the linear ordinary differential equations with polynomial coefficients they are solutions of. We compare the full set of singularities given by the roots of the head polynomial of these linear ODE's and the subset of singularities occurring in the integrals, with the singularities obtained from the Landau conditions. For these Ising class integrals, we show that the Landau conditions can be worked out, either to give the singularities of the corresponding linear differential equation or the singularities occurrin…

Algebras of singular integral operators on Nakano spaces with Khvedelidze weights over Carleson curves with logarithmic whirl points

We establish a Fredholm criterion for an arbitrary operator in the Banach algebra of singular integral operators with piecewise continuous coefficients on Nakano spaces (generalized Lebesgue spaces with variable exponent) with Khvedelidze weights over Carleson curves with logarithmic whirl points.

Logarithmic L^p bounds for maximal directional singular integrals in the plane

We discuss the L^p-boundedness of maximal singular integrals in the plane over a finite set V of N directions. Logarithmic bounds are established for a set V of arbitrary structure in the 2<=p<infinity range. Sharp bounds are proved for lacunary and Vargas sets of directions. The latter include the case of uniformly distributed directions and the finite truncations of the Cantor set. We make use of both classical harmonic analysis methods and product-BMO based time-frequency analysis techniques. As a further application of the latter, we derive an L^p almost orthogonality principle for Fourier…

关于奇异扰动 q-差分-微分方程中对数型解的 q-Gevrey 渐近性

On q-Gevrey asymptotics for logarithmic type solutions in singularly perturbed q-difference-differential equations

本文研究了一族奇异扰动 q-差分-微分方程，针对含形式单值性的全纯对数型解，通过构建 Borel 平面 Banach 空间乘积求不动点，并利用正阶 q-Gevrey 渐近展开描述了解的渐近行为。