21,031 research outputs found
Ramsey-like properties for bi-Lipschitz mappings of finite metric spaces
summary:Let , be metric spaces and an injective mapping. We put ; , , and (the {\sl distortion\/} of the mapping ). Some Ramsey-type questions for mappings of finite metric spaces with bounded distortion are studied; e.g., the following theorem is proved: Let be a finite metric space, and let , be given numbers. Then there exists a finite metric space , such that for every mapping ( arbitrary metric space) with one can find a mapping , such that both the mappings and have distortion at most . If is isometrically embeddable into a space (for some ), then also can be chosen with this property
Some remarks on harmonic projection operators on spheres
We give a survey of recent works concerning the mapping properties of joint harmonic projection operators, mapping the space of square integrable functions on complex and quaternionic spheres onto the eigenspaces of the Laplace-Beltrami operator and of a suitably defined subLaplacian. In particular, we discuss similarities and differences between the real, the complex and the quaternionic framework
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