Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth

Research Report MRR98-004

Spectral multipliers for a distinguished Laplacian on certain groups of exponential growth

Adam Sikora

Abstract: Let L be a distinguished Laplacian on an Iwasawa component AN=S of a non-compact, semi-simple Lie group or on a solvable extension S of an H-type group. We obtain a criterion for the

boundedness of a class of spectral multipliers of the operator L. The order of differentiability required is a half of the maximum of the dimension and the pseudo-dimension of the group S. We give examples of groups when this order of differentiability is optimal.

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