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).
Biography
Graduated from Faculty of Natural Sciences of E. Lorand Scientific University of Budapest in 1974 (speciality — physicist). Ph.D. thesis was defended in 1981. A list of my works contains more than 60 titles.
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.
V. N. Pyvovarchyk, “Ambarzumian's Theorem for a Sturm–Liouville Boundary Value Problem on a Star-Shaped Graph”, Funktsional. Anal. i Prilozhen., 39:2 (2005), 78–81; Funct. Anal. Appl., 39:2 (2005), 148–151
C. Van der Mee, V. N. Pyvovarchyk, “A Sturm–Liouville Inverse Spectral Problem with Boundary Conditions Depending on the Spectral Parameter”, Funktsional. Anal. i Prilozhen., 36:4 (2002), 74–77; Funct. Anal. Appl., 36:4 (2002), 315–317
V. N. Pyvovarchyk, “Reconstruction of the Potential of the Sturm–Liouville Equation from Three Spectra of Boundary Value Problems”, Funktsional. Anal. i Prilozhen., 33:3 (1999), 87–90; Funct. Anal. Appl., 33:3 (1999), 233–235
V. N. Pyvovarchyk, “On the Spectra of Small Vibrations of a String with Viscous Friction at One End”, Funktsional. Anal. i Prilozhen., 32:1 (1998), 78–81; Funct. Anal. Appl., 32:1 (1998), 61–63
G. M. Gubreev, V. N. Pyvovarchyk, “Spectral Analysis of the Regge Problem with Parameters”, Funktsional. Anal. i Prilozhen., 31:1 (1997), 70–74; Funct. Anal. Appl., 31:1 (1997), 54–57
V. N. Pyvovarchyk, “Necessary conditions for gyroscopic stabilization in a problem of mechanics”, Mat. Zametki, 53:6 (1993), 89–96; Math. Notes, 53:6 (1993), 622–627
N. D. Kopachevskii, V. N. Pyvovarchyk, “The sufficient condition for instability of the convective motion of a liquid in an open vessel”, Zh. Vychisl. Mat. Mat. Fiz., 33:1 (1993), 101–118; Comput. Math. Math. Phys., 33:1 (1993), 89–102
V. N. Pyvovarchyk, “Sufficient conditions for a weakly damped pencil to have a simple spectrum”, Sibirsk. Mat. Zh., 33:6 (1992), 201–204; Siberian Math. J., 33:6 (1992), 1131–1134
1991
9.
V. N. Pyvovarchyk, “On the total algebraic multiplicity of the spectrum in the right half-plane for a class of quadratic operator pencils”, Algebra i Analiz, 3:2 (1991), 223–230; St. Petersburg Math. J., 3:2 (1992), 447–454
10.
V. N. Pyvovarchyk, “Polynomial operator pencils connected with problems of mechanics”, Funktsional. Anal. i Prilozhen., 25:4 (1991), 62–64; Funct. Anal. Appl., 25:4 (1991), 281–282
1990
11.
V. N. Pyvovarchyk, “A spectral problem that is connected with an equation of viscous sound”, Differ. Uravn., 26:9 (1990), 1536–1541; Differ. Equ., 26:9 (1990), 1133–1137
12.
V. N. Pyvovarchyk, “Closedness of the approximate spectrum of a polynomial operator pencil”, Mat. Zametki, 47:6 (1990), 147–148
13.
V. N. Pyvovarchyk, “The discrete spectrum of a boundary value problem”, Sibirsk. Mat. Zh., 31:5 (1990), 182–186; Siberian Math. J., 31:5 (1990), 853–856
V. N. Pyvovarchyk, “Eigenvalues of a certain quadratic pencil of operators”, Funktsional. Anal. i Prilozhen., 23:1 (1989), 80–81; Funct. Anal. Appl., 23:1 (1989), 70–72
V. N. Pyvovarchyk, “The spectrum of quadratic operator pencils in the right half-plane”, Mat. Zametki, 45:6 (1989), 101–103
1988
16.
V. N. Pivovarchik, “On the number of eigenvalues of the Sturm–Liouville problem on the semiaxis with a potential that is linear with respect to the parameter”, Differ. Uravn., 24:4 (1988), 705–708
1987
17.
V. N. Pyvovarchyk, “The discrete spectrum of a problem connected with wave propagation in an inhomogeneous medium with viscous friction”, Differ. Uravn., 23:9 (1987), 1533–1538
18.
V. N. Pyvovarchyk, “A boundary value problem connected with oscillations of an elastic rod with internal and external friction”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1987, no. 3, 68–71
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