Speciality:
01.04.02 (Theoretical physics)
Birth date:
26.11.1950
E-mail: Keywords: inverse problems; Sturm–Liouville equation with boundary conditions dependent on the spectral parameter; Schroedinger equation on graphs; transversal vibrations of damped strings and beams; spectral theory of polynomial operator pencils; Riesz bases.
Subject:
The inverse Sturm–Liouville problem from three spectra of boundary problems was formulated and solved. Inverse problems for the Sturm–Liouville equation on simple graphs were solved. It was proved that the total algebraic multiplicity of the quadratic operator pencils spectrum located in the right half-plane is invariant under perturbations from certain class. Bases properties of eigenvalues of boundary problems describing damped strings were investigated (in collaboration with A. M. Gomilko).
Main publications:
Pivovarchik V. N., van der Mee C. The inverse generalized Regge problem // Inverse Problems, 2001, 17, 1831–1845.
Pivovarchik V. N. Inverse problem for the Sturm–Liouville equation on a simple graph // SIAM J. Math. Anal., 2000, 32(4), 801–819.
Pivovarchik V. N. Scattering in a loop-shaped waveguide // Operator Theory: Advances and Applications, 2001, 124, 527–543.
Pivovarchik V. N. An inverse Sturm–Liouville problem by three spectra // Integral Equations and Operator Theory, 1999, 34, 234–243.
Pivovarchik V. N. On positive spectra of one class of polynomial operator pencils // Integral equations and operator theory, 1994, 19, 314–326.
