{"date":"2022-09-14","starts":{"hour":14,"minute":0,"second":0,"second_of_day":50400},"ends":{"hour":15,"minute":0,"second":0,"second_of_day":54000},"room":"-101","speaker":"Or Elmakias","from":"BGU","title":"Constrained Pick interpolation for multiply connected domains","abstract":"The Pick interpolation theorem states that the existence of a function on the complex unit disc that is analytic, bounded by 1, and satisfies some interpolation data is equivalent to the positivity of a matrix that depends on the interpolation data. In 1979 Abrahamse generalized this result from the disk to any g-holed multiply connected domain. However, in the result of Aabrahamse, a family of matrices parametrized by the g-dimensional torus was needed. In 2010, A variation of the Pick interpolation problem was studied by Davidson, Paulsen, Raghupathi, and Singh, who discovered that if the constraint of zero derivative at a point is applied to the interpolating function, then there is a family of matrices parametrized by the unit sphere that need to be positive.\r\nIn my thesis, I have combined these results to solve a constrained interpolation problem on a multiply connected domain. I will present the ideas that prove these kinds of interpolation theorems, that were first applied to that cause by Sarason, and will show how I used them for the constraint-multiply connected problem. If time allows it, I will also say a few words about matrix-valued interpolation.","speaker_web":null,"announcement":null,"descfiles_signed_ids":"[]","online":false,"slug":"2022-09-14_14-00","shift":{"beginning":{"hour":14,"minute":0,"second":0,"second_of_day":50400},"ending":{"hour":15,"minute":0,"second":0,"second_of_day":54000},"exclude_end":false,"range":"[50400,54000]"},"announcement_i18n":{"en":"","he":""},"duration":"[2022-09-14 11:00:00 UTC,2022-09-14 12:00:00 UTC]","id":916,"created_at":"2022-09-13T10:49:32.154+03:00","updated_at":"2022-09-13T10:49:32.154+03:00","admin_users":[],"summary":"Or Elmakias: Constrained Pick interpolation for multiply connected domains","full_speaker_text":"Or Elmakias (*BGU*)","unusual":"day, time and place","unusual_place":true,"unusual_time":true,"unusual_day":true}