Curriculum Vitae of Volodymyr Koshmanenko
Date of birth: 28.07.1943
Professor, Leading Scientific Researcher
Department of Mathematical Physics
Institute of Mathematics
National Academy Sciences of Ukraine (NASU)
Address: Institute of
Mathemetics,
vul. Tereshchenkivs'ka 3, Kyiv, 01601 Ukraine
Tel.: 0038 044 2585872
(pr.)
Fax: 0038 044 2352010
E-mail: kosh@imath.kiev.ua, koshman63@googlemail.com
Main steps of career:
1960--1966 Dnipropetrovsk State University , Theoretical Physics
Department
1970 Ph.D. "Some questions of Quantum Field Theory"
(supervisor: Prof. Yu. M. Berezansky)
1984 Doctorate "Scattering Theory in Terms of Bilinear
Forms"
1970 -- up to present time: Institute of Matematics,
permanent position
Amount of publications:
over 100
Area of investigations: Quantum
Field Theory, Scattering Theory, Spectral Theory for Operators, Biliner
and Qudratic Forms, Theory of Singular Qudratic Forms, Singular
Perturbation Theory, Self-adjoint Extensions of Symmetric Operators,
Shrödinger Operators with Singular perturbations, Scales of
Hilbert Spaces, Fractal Structure of Spectrum, Dynamical Systems with
Conflict Interaction
Theaching activity:
1975 - 77, 2000 - 2005 Kyiv State University, Math. Analysis
Department
1980 - 1996 State Pedagogical University, Department of Higher
Math.
Main Results:
- Operator representation in a normal form by creation and
annihilation operators (the necessary and sufficient
- condition) (1969)
- The axiomatic quantum field in terms of Jacoby matrices
(1970)
- The Haag-Ruelle scattering theory in different state spaces
(1974-79)
- The scattering theory in terms of biliner functionals
(1975-79)
- Isomorphism between Fock space and infinite dimensional
functional space (1975)
- Canonical structure of wave operators (1979)
- The notion of singular
quadratic form (1979)
- Classification of singular quadratic forms in the scale of
Hilbert spaces (1982)
- Wave operators defined by the perturbed semi-group. The
scattering operator constructed inside of the Euclidean
approach (1984-85)
- The definition of the singular perturbed operator (1989)
- The theory of singular perturbation of self-adjoint
operators (1979-1993)
- Square power of singularly perturbed operators (1995)
- Regular restrictions of singular bilinear forms (1995)
- The Schrödinger operators with fractal and
- delta-potentials
(1990-2000)
- The method of orthogonal extension in singular perturbation
theory (1981, 1994)
- The Lippmann-Schwinger equation for singularly perturbed
operators (1997)
- The generalized sum of operators (1999)
- The form-sum approximation of singular perturbation of
self-adjoint operators (1999, 2000, 2003)
- The spectrum structure of generalized Laplace operators
(2001)
- The inverse spectral theory for singularly perturbed operators
(2002, 2005)
- The fine structure of the singular continuous spectrum (2003)
- The Aronszajn-Donoghue theory for rank one perturbations of
the H(-2)-class (2003)
- The point spectrum of the H (-2)-class singular perturbations
(2005,2007)
- The notion of the conflict composition for non-annihilating
opponents. Theorem of conflict for stochastic vectors and probability
measures (2003-2004)
- Description of limiting distributions in dynamical
systems with conflict interactions (2004)
- Spectral limiting properties of image measures under infinite
conflict interactions (2004, 2006)
- The construction of singular perturbations by the method of
rigged Hilbert spaces (2005)
- Models of the complex dynamical systems with conflict
interactions. Cyclic attractors. Interpretation in the terms of
migration (2006).