Spectral dilation of operator-valued measures and its application to infinite-dimensional harmonizable processes

A. Makagon; H. Salehi

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Spectral decompositions and harmonic analysis on UMD spaces

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We develop a spectral-theoretic harmonic analysis for an arbitrary UMD space X. Our approach utilizes the spectral decomposability of X and the multiplier theory for $L_{X}^{p}$ to provide on the space X itself analogues of the classical themes embodied in the Littlewood-Paley Theorem, the Strong Marcinkiewicz Multiplier Theorem, and the M. Riesz Property. In particular, it is shown by spectral integration that classical Marcinkiewicz multipliers have associated transforms acting on X. ...