Add to ORKGThere exist five families of Lipschitz curves on the unit square such that any continuous function is uniquely defined by the values of its integral (properly defined) along these curves. We present this uniqueness result as a consequence of the Kolmogorov’s superposition theorem. 1 Introduction1,2 The main intention of this article is to demonstrate a connection of results in Linear Superpositions of functions and the uniqueness problem for a gen-eralized Radon transform. We will actually present here one such relation, namely, a consequence of the Kolmogorov’s superposition theorem. We wil
A space of generalized functions is constructed that allows us to generalize Bochner\u27s theorem so...
We show that the normal operator of the X-ray transform in $\mathbb{R}^d$, $d\geq 2$, has a unique c...
AbstractA uniqueness theorem is proven for the problem of the recovery of a complex valued compactly...
Abstract. We consider a weighted Radon transform in the plane, Rm(ξ, η) =R R f(x, ξx + η)m(x, ξ, η)d...
We consider weighted Radon transforms $R_W$ along hyperplanes in $R^3$ with strictly positive weight...
We consider the weighted Radon transforms $R_W$ along hyperplanes in $R^d , \, d ≥ 3$, with strictly...
Let $S$ and the origin be different points of the closed curve $s$ in the plane. For any point $P$ t...
Abstract. These notes represent an extended version of the con-tents of the third lecture delivered ...
In recent work, methods from the theory of modular forms were used to obtain Fourier uniqueness resu...
Let $\Lambda$ be a set of lines in $\mathbb{R}^2$ that intersect at the origin. For $\Gamma\subset\m...
AbstractIn this work we consider two partial differential operators. We define a generalized Radon t...
We prove variable coefficient analogues of results in [5] on Hilbert transforms and maximal function...
A general framework to deal with problems of integral geometry is provided by the recently developed...
Linear integral transforms play an important role in many fields in physics. A transform of this kin...
We investigate the exponential Radon transform on a certain function space of generalized functions....
A space of generalized functions is constructed that allows us to generalize Bochner\u27s theorem so...
We show that the normal operator of the X-ray transform in $\mathbb{R}^d$, $d\geq 2$, has a unique c...
AbstractA uniqueness theorem is proven for the problem of the recovery of a complex valued compactly...
Abstract. We consider a weighted Radon transform in the plane, Rm(ξ, η) =R R f(x, ξx + η)m(x, ξ, η)d...
We consider weighted Radon transforms $R_W$ along hyperplanes in $R^3$ with strictly positive weight...
We consider the weighted Radon transforms $R_W$ along hyperplanes in $R^d , \, d ≥ 3$, with strictly...
Let $S$ and the origin be different points of the closed curve $s$ in the plane. For any point $P$ t...
Abstract. These notes represent an extended version of the con-tents of the third lecture delivered ...
In recent work, methods from the theory of modular forms were used to obtain Fourier uniqueness resu...
Let $\Lambda$ be a set of lines in $\mathbb{R}^2$ that intersect at the origin. For $\Gamma\subset\m...
AbstractIn this work we consider two partial differential operators. We define a generalized Radon t...
We prove variable coefficient analogues of results in [5] on Hilbert transforms and maximal function...
A general framework to deal with problems of integral geometry is provided by the recently developed...
Linear integral transforms play an important role in many fields in physics. A transform of this kin...
We investigate the exponential Radon transform on a certain function space of generalized functions....
A space of generalized functions is constructed that allows us to generalize Bochner\u27s theorem so...
We show that the normal operator of the X-ray transform in $\mathbb{R}^d$, $d\geq 2$, has a unique c...
AbstractA uniqueness theorem is proven for the problem of the recovery of a complex valued compactly...