相关论文: Stability estimates with a priori bound for the in…
We study the non-parametric estimation of a multidimensional unknown density f in a tomography problem based on independent and identically distributed observations, whose common density is proportional to the Radon transform of f. We…
We study estimation of a multivariate function $f:\mathbf{R}^d\to\mathbf{R}$ when the observations are available from the function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are…
We revisit the standard representation of the (inverse) Radon transform which is well-known in the mathematical literature. We extend this representation to the case involving the parton distributions. We have found the new additional…
An alternative method to invert the Radon transforms without the use of Courant-Hilbert's identities has been proposed and developed independently from the space dimension. For the universal representation of inverse Radon transform, we…
Let $F$ be a local field and $n\ge 2$ an integer. We study the Radon transform as an operator $M : \mathcal C_+ \to \mathcal C_-$ from the space of smooth $K$-finite functions on $F^n \setminus \{0\}$ with bounded support to the space of…
We are interested in an inverse medium problem with internal data. This problem is originated from multi-waves imaging. We aim in the present work to study the well-posedness of the inversion in terms of the boundary conditions. We…
In this article, we consider inverse problems of determining a source term and a coefficient of a first-order partial differential equation and prove conditional stability estimates with minimum boundary observation data and relaxed…
We continue to study the problem of modeling of substitution of production factors motivated by the need for computable mathematical models of economics that could be used as a basis in applied developments. This problem has been studied…
Let $\bbK=\mathbb R, \mathbb C, \mathbb H$ be the field of real, complex or quaternionic numbers and $M_{p, q}(\bbK)$ the vector space of all $p\times q$-matrices. Let $X$ be the matrix unit ball in $M_{n-r, r}(\bbK)$ consisting of…
Let $G\subset \C P^n$ be a linearly convex compact with smooth boundary, $D={\C}P^n\setminus G$, and let $D^* \subset (\C P^n)^*$ be the dual domain. Then for an algebraic, not necessarily reduced, complete intersection subvariety $V$ of…
The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…
We give an instability estimate for the Gel'fand inverse boundary value problem at high energies. Our instability estimate shows an optimality of several important preceeding stability results on inverse problems of such a type.
In this article, stability estimates are given for the determination of the zeroth-order bounded perturbations of the biharmonic operator when the boundary Neumann measurements are made on the whole boundary and on slightly more than half…
This article presents extensions of the Cram{\'e}r-Wold theorem to measures that may have infinite mass near the origin. Corresponding results for sequences of measures are presented together with examples showing that the assumptions…
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
In this paper we prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in $\mathbb{R}^n$, from a knowledge, in a finite time observation, of…
The spherical Radon-Dunkl transform $R_\kappa$, associated to weight functions invariant under a finite reflection group, is introduced, and some elementary properties are obtained in terms of $h$-harmonics. Several inversion formulas of…
We find sharp conditions for the maximal operator associated with generalized spherical mean Radon transform on radial functions $M^{\a,\b}_t$ to be bounded on power weighted Lebesgue spaces. Moreover, we also obtain the corresponding…
We give new stability estimates for the Gel'fand-Calderon inverse boundary value problem
Let $\Omega\subset\mathbb{R}^3$ be a domain and let $f\in BV_{\operatorname{loc}}(\Omega,\mathbb{R}^3)$ be a homeomorphism such that its distributional adjugate is a finite Radon measure. We show that its inverse has bounded variation…