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By Syed T. Ali, J-P. Antoine, Jean-Perre Gazeau

A survey of the idea of coherent states, wavelets, and a few in their generalizations, emphasizing mathematical constructions. ranging from the normal concept of coherent states over Lie teams, the authors generalize the formalism by way of associating coherent states to staff representations which are sq. integrable over a homogeneous house; one other step permits the crowd context to be allotted with altogether. The unified heritage makes obvious differently vague houses of wavelets and of coherent states. Many concrete examples, equivalent to semisimple Lie teams, the relativity workforce, and several other varieties of wavelets, are mentioned intimately. The e-book concludes with actual functions, centering at the quantum dimension challenge and the quantum-classical transition. meant as an creation to present study for graduate scholars and others getting into the sector, the mathematical dialogue is self- contained. With its vast references to the examine literature, the ebook can also be an invaluable compendium of contemporary effects for physicists and mathematicians already energetic within the box.

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This mode of presentation should not be taken as implying that I subscribe to a heroic theory of either 14 Prologue technological or organizational change. It does reflect a belief that, al­ though the development of technology and the rise of complex hierar­ chical organizations can be depicted as historical forces that transcend individual personalities, nevertheless they work themselves out through the decisions of individual men and women, and there is a certain gain in directness and immediacy when we show this process in operation.

In Syntony and Spark it had been possible to use a biographical approach almost exclusively. Hertz, Lodge, Marconi—these were unambiguously the individuals responsible for the "translations" that made a commercial communications system out of 22 Prologue Maxwell's equations. Formal organizations played a certain role—Mar­ coni's Wireless Telegraph Company, the British Post Office—but they remained largely in the background. As the story moved into the twentieth century, however, this would no longer do.

The entry of large cor­ porations into continuous wave radio, best symbolized by AT&T's pur- Prologue 23 chase of de Forest's audion patents in 1912 and GE's creation of RCA in 1919, represented attempts to bring the new technology under control, to develop it in directions that would further corporate interests and control its use in areas where it might threaten those interests. Longterm capital could be assured; predictable markets could be guaranteed (or so it was thought); and the organized intelligence of corporate re­ search laboratories could be mobilized to perfect and extend what in­ dividual inventors had created.

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