Variation and oscillation for harmonic operators in the inverse Gaussian setting

Darboux transforms of a harmonic inverse mean curvature surface

The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward Bäcklund transform of a generalized harmonic inverse mean curvature surface is defined. A Darboux transform of a generalized harmonic inverse mean curvature surface is constructed by a backward Bäcklund transform. For a given isothermic harmonic inverse mean curvature surface, its classical Darboux transform is a harmonic inverse mean curvature surface. Then a transform of a solution to the Painlevé III equation in trigonometric form is defined by a classical Darboux transf…

Boundary oscillations of harmonic functions in Lipschitz domains

Let $u(x,y)$ be a harmonic function in the halfspace $\mathbb{R}^n\times\mathbb{R}_+$ that grows near the boundary not faster than some fixed majorant $w(y)$. Recently it was proven that an appropriate weighted average along the vertical lines of such a function satisfies the Law of Iterated Logarithm (LIL). We extend this result to a class of Lipschitz domains in $\mathbb{R}^{n+1}$. In particular, we obtain the local version of this LIL for the upper halfspace. The proof is based on approximation of the weighted averages by a Bloch function, satisfying some additional condition determined by …

双曲反正弦核、有限傅里叶滤波器和四次中心二项式调和和

Arcsine kernels, inverse-binomial harmonic sums, and classical hypergeometric transformations

研究将反正弦幂展开相关系数族放入双曲反正弦核，通过有限傅里叶投影和梅林变形等方法，得到含特定参数的恒等式及相关结果，还记录了核间卷积等细节，指出直接四次核会导致不同的\({}_4F_3\)族。