اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدFrames of p-adic wavelets and orbits of the affine group
131
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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
e fact that the group does not act on the phase space. However it is possible to define its action on some classes of functions.
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
e listed for all cases n<=8 and for the infinite series of algebra-subalgebra pairs A(n) - A(n-k-1) x A(k) x U(1), A(2n) - B(n), A(2n-1) - C(n), A(2n-1) - D(n). Numerous special cases and examples are shown.
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 lower semi-frame has an unbounded frame operator, with bounded inverse. For upper semi-frames, in the discrete and the continuous case, we build two natural Hilbert scales which may yield a novel characterization of certain function spaces of interest in signal processing. We present some examples and, in addition, some results concerning the duality between lower and upper semi-frames, as well as some generalizations, including fusion semi-frames and Banach semi-frames.
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
ing the Dirac delta functions $delta_{x}$ concentrated on points ${x_1,...,x_n}$ of the field of $p$-adic numbers $mathbb{Q}_p$. It is shown that such a problem is well-posed for $alpha>1/2$ and the singular perturbation $V_Y$ is form-bounded for $alpha>1$. In the latter case, the spectral analysis of $eta$-self-adjoint operator realizations of $D^{alpha}+V_Y$ in $L_2(mathbb{Q}_p)$ is carried out.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
