Related papers: On the McLaughlin-Rundell theorem
Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…
The note contains the proof of the uniqueness theorem for the inverse problem in the case of $n$-th order differential equation.
We prove Marchenko-type uniqueness theorems for inverse Sturm-Liouville problems. Moreover, we prove a generalization of Ambarzumyans theorem.
We establish two theorems that illustrate the uniqueness of inverse q-Sturm-Liouville problems based on a specified set of spectral data. The first uniqueness theorem employs the method of transformation operators to provide a q-analog of…
In a unitary ring with involution, we prove that each element has at most one weak group inverse if and only if each idempotent element has a unique weak group inverse. Furthermore, we define the $m$-weak group inverse and show some…
An integro-differential Dirac system with an integral term in the form of convolution is considered. We suppose that the convolution kernel is known a priori on a part of the interval, and recover it on the remaining part, using a part of…
A counterexample is given to the uniqueness result given in the paper by J.Cox and K.Thompson, "Note on the uniqueness of the solution of an equation of interest in inverse scattering problem", J. Math.Phys., 11, N3, (1970), 815-817.
We prove a uniqueness theorem for an inverse boundary value problem for the Maxwell system with boundary data assumed known only in part of the bound- ary. We assume that the inaccessible part of the boundary is either part of a plane, or…
We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.
In this paper, we prove an existence and uniqueness theorem for orientation-reversing harmonic diffeomorphisms from $\mathbb{H}_*^n$ to $\mathbb{R}_*^n$ with rotational symmetry, which is a generalization of the corresponding result for…
We show that there exists an uniformly recurrent infinite word whose set of factors is closed under reversal and which has only finitely many palindromic factors.
An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…
In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system…
We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.
We present a short proof of the gauge invariant uniqueness theorem for relative Cuntz-Pimsner algebras of C*-correspondences.
We prove a simple inequality for a sum of squares of norms of two vectors in an inner product space. Next, using this inequality we derive the so--called "reverse uncertainty relation" and analyze its properties.
We correct the proof of Theorem 4.1 from [C. R. Math. Acad. Sci. Soc. R. Can. \textbf{44} (2022), no. 4, 88--112].
In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic…
In this paper, we discuss uniqueness and backward uniqueness for mean curvature flow of non-compact manifolds. We use an energy argument to prove two uniqueness theorems for mean curvature flow with possibly unbounded curvatures. These…
This research was devoted to investigate the inverse spectral problem of Sturm-Liouville operator with many frozen arguments. Under some assumptions, the authors obtained uniqueness theorems. At the end, a numerical simulation for the…