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We consider inverse boundary value problems for polyharmonic operators and in particular, the problem of recovering the coefficients of terms up to order one. The main interest of our result is that it further relaxes the regularity…
In this work, we study the inverse spectral problem, using the Weyl matrix as the input data, for the matrix Schrodinger operator on the half-line with the boundary condition being the form of the most general self-adjoint. We prove the…
The operator of double differentiation, perturbed by the composition of the differentiation operator and a convolution one, on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the…
The paper deals with nonlocal differential operators possessing a term with frozen (fixed) argument appearing, in particular, in modelling various physical systems with feedback. The presence of a feedback means that the external affect on…
We consider a second order functional-differential pencil with two constant delays of the argument and study the inverse problem of recovering its coefficients from the spectra of two boundary value problems with one common boundary…
This work deals with an inverse problem for the Sturm-Liouville operator with non-separated boundary conditions, one of which linearly depends on a spectral parameter. Uniqueness theorem is proved, solution algorithm is constructed and…
In this paper we discuss an abstract iteration scheme for the calculation of the smallest eigenvalue of an elliptic operator eigenvalue problem. A short and geometric proof based on the preconditioned inverse iteration (PINVIT) for matrices…
New index transforms, involving the real part of the modified Bessel function of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue…
We consider an eigenvalue problem for an inverted one dimensional harmonic oscillator. We find a complete description for the eigenproblem in $C^{\infty}(\mathbb R)$. The eigenfunctions are described in terms of the confluent hypergeometric…
We examine inverse problems for the variable-coefficient nonlocal parabolic operator $(\partial_t - \Delta_g)^s$, where $0 < s < 1$. This article makes two primary contributions. First, we introduce a novel entanglement principle for these…
We study an inverse problem involving the unique recovery of several lower order anisotropic tensor perturbations of a polyharmonic operator in a bounded domain from the knowledge of the Dirichlet to Neumann map on a part of boundary. The…
Motivated by a recent study of Bessel operators in connection with a refinement of Hardy's inequality involving $1/\sin^2(x)$ on the finite interval $(0,\pi)$, we now take a closer look at the underlying Bessel-type operators with more…
In this paper we consider a twofold Ellis-Gohberg type inverse problem in an abstract *-algebraic setting. Under natural assumptions, necessary and sufficient conditions for the existence of a solution are obtained, and it is shown that in…
We consider an inverse spectral problem for radial Schr\"odinger operators with singular potentials. First, we show that the knowledge of the Dirichlet spectra for infinitely many angular momenta~$\ell$ satisfying a M\"untz-type condition…
The transmutation (transformation) operator associated with the perturbed Bessel equation is considered. It is shown that its integral kernel can be uniformly approximated by linear combinations of constructed here generalized wave…
The inverse problem for the differential operator pencil with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator…
This article offers a study of the Calder\'on type inverse problem of determining up to second order coefficients of the higher order elliptic operator. Here we show that it is possible to determine an anisotropic second order perturbation…
Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range or exponentially decaying perturbation of a periodic Jacobi operator. As a corollary we can fully solve the inverse resonance…
Boundary value problems on hedgehog-type graphs for Sturm-Liouville differential operators with general matching conditions are studied. We investigate inverse spectral problems of recovering the coefficients of the differential equation…
Inverse spectral problems for Sturm-Liouville operators with nonlocal boundary conditions are studied. As the main spectral characteristics we introduce the so-called Weyl-type function and two spectra, which are generalizations of the…