arXiv subjects

Yingzhan Wang

Publications and source records attributed to Yingzhan Wang.

5 recordsLinked to original sources

arXiv2021

Strichartz transforms with Riesz potentials and Semyanistyi integrals

In this paper, we study the general orthogonal Radon transform $R_{p,q}^k$ first studied by R.S Strichartz in \cite{Stri}. An sharp existence condition of $R_{p,q}^k f$ on $L^p$-spaces will be given. Then we devote to the relation formulas connecting Strichartz transform $R_{p,q}^k$ and Semyanistyi integrals. We prove the corresponding Fuglede type formulas, through which a number of explicit inversion formulas for $R_{p,q}^k f$ will be given. Different from the inclusion Radon transform and "Gonzalez" type orthogonal transform, Strichartz transform is more complicated. Our conclusions generalize the corresponding results of the two particular cases above.

math.FA↗

arXiv2019

Radon Transforms for Mutually Orthogonal Affine Planes

We study a Radon-like transform that takes functions on the Grassmannian of $j$-dimensional affine planes in $\Bbb R ^n$ to functions on a similar manifold of $k$-dimensional planes by integration over the set of all $j$-planes that meet a given $k$-plane at a right angle. The case $j=0$ gives the classical Radon-John $k$-plane transform. For any $j$ and $k$, our transform has a mixed structure combining the $k$-plane transform and the dual $j$-plane transform. The main results include action of such transforms on rotation invariant functions, sharp existence conditions, intertwining properties, connection with Riesz potentials and inversion formulas in a large class of functions. The consideration is inspired by the previous works of F. Gonzalez and S. Helgason who studied the case $j+k=n-1$, $n$ odd, on smooth compactly supported functions.

math.FA↗

arXiv2016

New Inversion Formulas for Radon Transforms on Affine Grassmannians

We obtain new inversion formulas for the Radon transform and the corresponding dual transform acting on affine Grassmann manifolds of planes in $R^n$. The consideration is performed in full generality on continuous functions and functions belonging to $L^p$ spaces.

math.FA↗

arXiv2016

On Radon transforms between lines and hyperplanes

We obtain new inversion formulas for the Radon transform and its dual between lines and hyperplanes in $\rn$. The Radon transform in this setting is non-injective and the consideration is restricted to the so-called quasi-radial functions that are constant on symmetric clusters of lines. For the corresponding dual transform, which is injective, explicit inversion formulas are obtained both in the symmetric case and in full generality. The main tools are the Funk transform on the sphere, the Radon-John $d$-plane transform in $\rn$, the Grassmannian modification of the Kelvin transform, and the Erdélyi-Kober fractional integrals.

math.FA↗

arXiv2013

Wiener measure for Heisenberg group

In this paper, we build Wiener measure for the path space on the Heisenberg group by using of the heat kernel corresponding to the sub-Laplacian and give the definition of the Wiener integral. Then we give the Feynman-Kac formula.

math.FA↗