Jan Janas, professor
Ph. D.: UJ 1973, habilitation: IM PAN 1977
In recent years my interests center around unbounded hyponormal operators and
unbounded Toeplitz operators in the Segal-Bargmann space. Another related
area I am interested in is theory of band matrices (in particular Jacobi).
All the above areas have some useful connections which I try to exploit.
- Alternative approaches to asymptotic
behaviour of eigenvalues of some unbounded Jacobi matrices
(with Maria Malejki), J. Comput. Appl. Math. (to appear)
- The asymptotic analysis of generalized
eigenvectors of some Jacobi operators. Jordan box case,
J. Difference Equ. Appl. 12 (2006), 597618.
- New discrete Levinson type asymptotics of
solutions of linear systems (with Marcin Moszyński),
J. Difference Equ. Appl. 12 (2006), 133163.
- Infinite Jacobi matrices with unbounded entries: asymptotics of
eigenvalues and the transformation operator approach
(with Serguei Naboko), SIAM J. Math. Anal. 36 (2004), 643658
- Spectral gaps resulting from periodic perturbations of a class of Jacobi
operators (with J. Dombrowski, M. Moszyński, S. Pedersen)
Constr. Approx. 20 (2004), 585601.
theory for a class of periodically perturbed unbounded Jacobi matrices:
elementary methods (with Serguei Naboko, Gunter Stolz),
J. Comput. Appl. Math. 171 (2004), 265276.
- Spectral properties of Jacobi matrices by asymptotic analysis
(with Marcin Moszyński),
J. Approx. Theory 120 (2003), 309336.
- Spectral analysis of selfadjoint Jacobi matrices with periodically
modulated entries (with Serguei Naboko), J. Funct. Anal. 191 (2002),
- Alternative approaches to the absolute continuity of Jacobi matrices
with monotonic weights (with Marcin Moszyński),
Integral Equations Operator Theory 43 (2002), 397416.
- Asymptotics of generalized eigenvectors for unbounded Jacobi matrices
with power-like weights, Pauli matrices commutation relations and Cesaro
averaging (with Serguei Naboko),
in: Differential operators and related topics, Vol. I (Odessa, 1997),
165186, Oper. Theory Adv. Appl. 117,
Birkhäuser, Basel, 2000.
- Jacobi matrices with power-like weights grouping in blocks approach
(with Serguei Naboko), J. Funct. Anal. 166 (1999), no. 2, 218243.
- Jacobi matrices with absolutely continuous spectrum
(with Serguei Naboko), Proc. Amer. Math. Soc. 127 (1999), 791800.
- Selfadjoint operator matrices with finite rows
(with Jan Stochel), Ann. Polon. Math. 66 (1997), 155172
(Volume dedicated to the memory of Włodzimierz Mlak).
- On Unbounded Hyponormal Operators I, II, III, Ark. Math.
27 (1989) 273281, Integral Equat. Op. Th. 15 (1992), 470478,
Studia Math. 112 (1994), 7582.
- Unbounded Toeplitz Operators in the Segal-Bargmann Space I, II
(with J. Stochel), Studia Math. 99 (1991) 8799, J. Funct. Anal.
126 (1994), No. 2, 418447.