Viazovska M. Inequalities for rational functions and polynomials and quadrature formulas on a sphere

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0410U002284

Thesis Registration Form

0410U002284.pdf

Applicant for

Specialization

  • 01.01.01 - Математичний аналіз

11-05-2010

Specialized Academic Board

Д 26.206.01

The Institute of Mathematics of NASU

Essay

This work contains new results concerning the monotone rational approximation, polynomial kernels and spherical designs. We establish Bernstein type inequality for the derivative of a monotone rational function using uniform norm of function on the right hand side. We obtain an explicit formula for the normalizing multiple of the generalized Jackson kernel and prove an asymptotically exact estimate for its value. We give two new constructions of spherical designs. These constructions improve known asymptotic upper bounds for the minimal number of points in a spherical design.

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Files

aref.pdf

dis.pdf

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