Учкай маалымат
In this book, we discuss in detail two major topics: exactly solvable linear differential operators, closely related to the Bochner–Krall problem in orthogonal polynomials, and the (generalized) Heine–Stieltjes theory, both of which originated more than a century ago. Our main emphasis is on the study of the root asymptotics of various polynomial sequences appearing in both problems. We also establish connections between our asymptotic analysis and special classes of quadratic and higher-order differentials, as well as other objects of geometric origin. In addition, we present a wealth of numerical results and suggest many open problems for the interested reader.
Дагы башкалар
Автор жөнүндө
Prof. B.Shapiro has been working in Stockholm University since 1991. He has published around 130 articles in various areas of mathematics, mainly in differential equations, topology and commutative algebra. One of his (joint) achievements is the formulation of the so-called Shapiro-Shapiro conjecture in real Schubert calculus which has been later settled by Mukhin-Tarasov-Varchenko. Another is his finding of a very intriguing, but completely forgotten conjecture on the number of equilibrium points for systems of point charges in 3-dimensional space due to J.C.Maxwell which was published in his book “A Treatise on Electricity and Magnetism” in 1873.
Prof. B.Shapiro is a permanent recipient of research grants from the Swedish Science Foundation and served as an advisor for 12 doctoral students.
