TY - JOUR
T1 - NON-ARCHIMEDEAN ANALOGUE OF THE SPACE OFVALUATIONS ON CONVEX SETS
AU - ALESKER, Semyon
N1 - Publisher Copyright:
© Copyright 2025.
PY - 2025
Y1 - 2025
N2 - In the last two decades a number of structures on the classical space of translation invariant valuations on convex bodies were discovered, e.g. product, convolution, a Fourier type transform. In this paper a non-Archimedean analogue of the space of such (even) valuations with similar structures is constructed. It is shown that, like in the classical case, the new space equipped with either product or convolution satisfies Poincaré duality and hard Lefschetz theorem.
AB - In the last two decades a number of structures on the classical space of translation invariant valuations on convex bodies were discovered, e.g. product, convolution, a Fourier type transform. In this paper a non-Archimedean analogue of the space of such (even) valuations with similar structures is constructed. It is shown that, like in the classical case, the new space equipped with either product or convolution satisfies Poincaré duality and hard Lefschetz theorem.
UR - https://www.scopus.com/pages/publications/105023964954
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AN - SCOPUS:105023964954
SN - 2189-3756
VL - 10
SP - 1089
EP - 1132
JO - Pure and Applied Functional Analysis
JF - Pure and Applied Functional Analysis
IS - 5
ER -