Jan Janas, professor

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.

Selected Publications:

• 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), 597–618.
• New discrete Levinson type asymptotics of solutions of linear systems (with Marcin Moszyński), J. Difference Equ. Appl. 12 (2006), 133–163.
• Infinite Jacobi matrices with unbounded entries: asymptotics of eigenvalues and the transformation operator approach (with Serguei Naboko), SIAM J. Math. Anal. 36 (2004), 643–658 (electronic)
• Spectral gaps resulting from periodic perturbations of a class of Jacobi operators (with J. Dombrowski, M. Moszyński, S. Pedersen) Constr. Approx. 20 (2004), 585–601.
• Spectral theory for a class of periodically perturbed unbounded Jacobi matrices: elementary methods (with Serguei Naboko, Gunter Stolz), J. Comput. Appl. Math. 171 (2004), 265–276.
• Spectral properties of Jacobi matrices by asymptotic analysis (with Marcin Moszyński), J. Approx. Theory 120 (2003), 309–336.
• Spectral analysis of selfadjoint Jacobi matrices with periodically modulated entries (with Serguei Naboko), J. Funct. Anal. 191 (2002), 318–342.
• Alternative approaches to the absolute continuity of Jacobi matrices with monotonic weights (with Marcin Moszyński), Integral Equations Operator Theory 43 (2002), 397–416.
• 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), 165–186, 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, 218–243.
• Jacobi matrices with absolutely continuous spectrum (with Serguei Naboko), Proc. Amer. Math. Soc. 127 (1999), 791–800.
• Selfadjoint operator matrices with finite rows (with Jan Stochel), Ann. Polon. Math. 66 (1997), 155–172 (Volume dedicated to the memory of Włodzimierz Mlak).
• On Unbounded Hyponormal Operators I, II, III, Ark. Math. 27 (1989) 273–281, Integral Equat. Op. Th. 15 (1992), 470–478, Studia Math. 112 (1994), 75–82.
• Unbounded Toeplitz Operators in the Segal-Bargmann Space I, II (with J. Stochel), Studia Math. 99 (1991) 87–99, J. Funct. Anal. 126 (1994), No. 2, 418–447.