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Vladimir Protasov
| Speaker: |
Vladimir Protasov (Moscow State University, Russia)
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| Date: |
Wednesday June 27, 2007
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| Title: |
Power random
series and wavelets. What is in common?
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Abstract
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The
problem of distributions of power random series has been known since
the famous works of P.Erdos and it has found many applications in the
study of functional equations, random walks on a real line, Bernoulli
convolutions, etc. Suppose we have a power series, whose coefficients
are independent identically distributed random
variables. The problem is to determine, whether such
a series has a density, or is it singular ? Surprisingly, one
special case of this problem leads to the so-called refinement equation
(functional difference equation with the contraction of an argument),
which is applied in the construction of wavelets.
Solvability of this equation is equivalent to the existence of the
distribution density. This phenomenon explains many common properties
of wavelets and distributions of random series.
Basic definitions, a detailed introduction and historical background
will be given in the lecture.
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