A large part of the structure of the objects in the theory of Dooley and Wildberger [Funktsional. Anal. I Prilozhen. 27 (1993), no. 1, 25-32] and that of Rouviere [Compositio Math. 73 (1990), no. 3, 241-270] can be described by considering a connected, finite-dimentional symmetric space G/H (as defined by Rouviere), with ???exponential map???, Exp, from L G/L H to G/H, an action, ???: K ??? Aut??(G) (where Aut?? (G) is the projection onto G/H of all the automorphisms of G which leave H invariant), of a Lie group, K, on G/H and the corresponding action, ???# , of K on L G/L H defined by g ??? L (???g), along with a quadruple (s, E, j, E#), where s is a ???# - invariant, open neighbourhood of 0 in L G/L H, E is a test-function subspace of C??? (Exp s), j ?? C??? (s), and E# is a test-function subspace of C??? (s) which contains { j.f Exp: f ?? E }. Of interest is the question: Is the function ???: ?? ??? ????, where ??: f ??? j.f Exp, a local associative algebra homomorphism from F# with multiplication defined via convolution with respect to a function e: s x s ??? C, to F, with the usual convolution for its multiplication (where F is the space of all ??? - invariant distributions of E and F# is the space of all ???# - invariant distributions of E#)? For this system of objects, we can show that, to some extent, the choice of the function j is not critical, for it can be ???absorbed??? into the function e. Also, when K is compact, we can show that ??? ker ?? = { f ?? E : ???k f (???g) dg = 0}. These results turn out to be very useful for calculations on s2 ??? G/H, where G = SO(3) and H??? SO(3) with H ??? SO(2) with ??? : h ??? Lh, as we can use these results to show that there is no quadruple (s, E, j, E#) for SO(3)/H with j analytic in some neighbourhood of 0 such that ??? is a local homomorphism from F# to F. Moreover, we can show that there is more than one solution for the case where s, E and E# are as chosen by Rouviere, if e is does not have to satisfy e(??,??) = e(??,??).

Thesis (M. Sc.)--University of Adelaide, Dept of Pure Mathematics,1984. / Includes bibliographical references (leaves 69-72).

Thesis (Ph. D.)--University of Adelaide, Dept. of Pure Mathematics, 1984. / Includes bibliographical references.

Thesis (Ph. D.)--University of New South Wales, 1999. / Includes bibliographical references and index. Also available online.

Thesis (M. S.)--Economics, Georgia Institute of Technology, 2008. / Committee Chair: Ghosal, Vivek; Committee Member: Iacopetta, Maurizio; Committee Member: Kilic, Rehim.

Dissertation (Ph.D.)--Auburn University, 2008. / Abstract.

Thesis (doctoral)--Universität, Münster, 2009. / Includes bibliographical references.

Proefschrift--Eindhoven. / "Stellingen": [6] p. inserted. Summary in Dutch. Bibliography: p. 77-78.

Thesis--Bonn. / Extra t.p. with thesis statement inserted. Includes bibliographical references.

Bachelor-Arbeit Univ. St. Gallen, 2004.