Computational Methods and Function Theory 6 (2006), No. 1, 183--201
Copyright Heldermann Verlag 2006
Anatolii Grinshpan
agrinsh@math.okstate.edu , Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, U.S.A.
We discuss the monotonicity aspect and derive inequalities for vector functions that satisfy a general matrix ODE. The study is motivated by the properties of the subordination chains of analytic functions and by the de Branges treatment of Loewner's equation.
Keywords: Linear differential operators, Loewner-Kufarev equation, subordination chains of analytic functions, de Branges' weights, Legendre polynomials and associated functions, cosine expansions with positive coefficients.
MSC 2000: 34L99, 30C50, 30C55, 30C75, 33C55.
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