On 03.05.2017, at 15.00, at the Institute seminar prof. of M.V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Department of Mathematical Analysis, Mirzoyev K.A. will give a talk on “Generalized Jacobian matrices as matrix representation of ordinary differential operators with polynomial coefficients”.
The lecture deals with matrix representation of minimal differential operators generated by linear differential expressions with polynomial coefficients in the space L₂(-∞;+∞) The cases when the coefficient at higher derivative of differential expression has zeroes, i.e. the cases of irregular differential expressions are not excluded. It is known that the Chebyshev-Hermite functions are the basis of matrix representation of these operators, and as a result the generalized Jacobian matrices are obtained (see e.i. A.G. Kostynchenko, K.A. Mirzoyev’spaper // Funksionalniyanaliz I ego pril., 1999, vol. 33, issue 1, p. 30-45). Such a representation in the case of symmetric differential expressions admits to construct n –th order entire differential operators in M.G. Krein’s sense, with defective numbers  (m,m) and m>n is also possible.
Some unsolved problems from spectral theory of ordinary differential operators, are also stated.

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