Weighted Strongly Elliptic Operators on Lie Groups

On Strongly $H_{v}$-groups

‎The largest class of hyperstructures is the one which satisfies the weak properties; these are called $H_{v}$-structures‎. ‎In this paper we introduce a special product of elements in $H_{v}$-group $H$ and define a new class of $H_{v}$-groups called strongly $H_{v}$-groups‎. ‎Then we show that in strongly $H_{v}$-groups $beta=beta^{ast}$‎. ‎Also we express $theta$-hyperoperation and investigat...

Bounds for Elliptic Operators in Weighted Spaces

An Index Theorem for Families Elliptic Operators Invariant with Respect to a Bundle of Lie Groups

We define the equivariant family index of a family of elliptic operators invariant with respect to the free action of a bundle G of Lie groups. In this paper we concentrate on the issues specific to the case when G is trivial, so the action reduces to the action of a Lie group G. For G simply-connected solvable, we then compute the Chern character of the (equivariant family) index, the result b...

Operators on Diierential Forms for Lie Transformation Groups

For any Lie group action S: GP ! P , we introduce C 1 (P)

-bounds for Pseudo-differential Operators on Compact Lie Groups

Given a compact Lie group G, in this paper we establish L p-bounds for pseudo-differential operators in L p(G). The criteria here are given in terms of the concept of matrix symbols defined on the noncommutative analogue of the phase space G× Ĝ, where Ĝ is the unitary dual of G. We obtain two different types of L p bounds: first for finite regularity symbols and second for smooth symbols. The c...