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The general construction of frames of p-adic wavelets is described. We consider the orbit of a mean zero generic locally constant function with compact support (mean zero test function) with respect to the action of the p-adic affine group and show that this orbit is a uniform tight frame. We discuss relation of this result to the multiresolution wavelet analysis.
We introduce an infinite-dimensional $p$-adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by th
An overview is given on recent developments in the affine Weyl group approach to Painleve equations and discrete Painleve equations, based on the joint work with Y. Yamada and K. Kajiwara.
The orbits of Weyl groups W(A(n)) of simple A(n) type Lie algebras are reduced to the union of orbits of the Weyl groups of maximal reductive subalgebras of A(n). Matrices transforming points of the orbits of W(An) into points of subalgebra orbits ar
Given a total sequence in a Hilbert space, we speak of an upper (resp. lower) semi-frame if only the upper (resp. lower) frame bound is valid. Equivalently, for an upper semi-frame, the frame operator is bounded, but has an unbounded inverse, whereas
A $p$-adic Schr{o}dinger-type operator $D^{alpha}+V_Y$ is studied. $D^{alpha}$ ($alpha>0$) is the operator of fractional differentiation and $V_Y=sum_{i,j=1}^nb_{ij}<delta_{x_j}, cdot>delta_{x_i}$ $(b_{ij}inmathbb{C})$ is a singular potential contain