Wavelets for quantum gravity and divergence-free wavelets. (Letter to the editor). (English) Zbl 0798.42024

Battle, Guy; Federbush, Paul; Uhlig, Paul

Appl. Comput. Harmon. Anal. 1, No. 3, 295-297 (1994).

Summary: We present an easy construction of \(L^ 2\)-orthonormal bases of divergence-free wavelets in two, four, and eight dimensions. Both wavelets of class \(C^ M\) with exponential decay and wavelets of the Meyer type are constructed. The idea is extended to the construction of symmetric-tensor-valued, divergence-free, trace-free wavelets in four dimensions – of both types. Such orthonormal bases could be applicable to quantum gravity.

MSC:

42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems
81V17	Gravitational interaction in quantum theory

Keywords:

symmetric tensor valued wavelets; \(L^ 2\)-orthonormal bases; divergence- free wavelets; exponential decay; trace-free wavelets; four dimensions