{"id":12580,"date":"2017-05-04T12:32:37","date_gmt":"2017-05-04T08:32:37","guid":{"rendered":"http:\/\/www.imm.az\/exp\/?p=12580"},"modified":"2017-05-04T12:32:37","modified_gmt":"2017-05-04T08:32:37","slug":"the-institute-seminar-on-generalized-jacobian-matrices-as-matrix-representation-of-ordinary-differential-operators-with-polynomial-coefficients","status":"publish","type":"post","link":"https:\/\/www.imm.az\/exp\/2017\/05\/04\/the-institute-seminar-on-generalized-jacobian-matrices-as-matrix-representation-of-ordinary-differential-operators-with-polynomial-coefficients\/","title":{"rendered":"The institute seminar on\u00a0\u201cGeneralized Jacobian matrices as matrix representation of ordinary differential operators with polynomial coefficients\u201d"},"content":{"rendered":"

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. gave a talk on \u201cGeneralized Jacobian matrices as matrix representation of ordinary differential operators with polynomial coefficients\u201d.
\nThe lecture deals with matrix representation of minimal differential operators generated by linear differential expressions with polynomial coefficients in the space L2<\/sub><\/em>(-\u221e;+\u221e) 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\u2019spaper \/\/ 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\u00a0–<\/em>th order entire differential operators in M.G. Krein\u2019s sense, with defective numbers \u00a0(m,m<\/em>) and\u00a0m>n\u00a0<\/em>is also possible.
\nSome unsolved problems from spectral theory of ordinary differential operators, are also stated.<\/p>\n