Download PDF by Armand Borel: Automorphic forms on SL₂(R)

By Armand Borel

ISBN-10: 0521072123

ISBN-13: 9780521072120

ISBN-10: 0521580498

ISBN-13: 9780521580496

This booklet presents an creation to a few facets of the analytic thought of automorphic varieties on G=SL2(R) or the upper-half airplane X, with appreciate to a discrete subgroup ^D*G of G of finite covolume. the perspective is galvanized by means of the idea of countless dimensional unitary representations of G; this is often brought within the final sections, making this connection specific. the subjects handled comprise the development of primary domain names, the concept of automorphic shape on ^D*G\G and its courting with the classical automorphic varieties on X, Poincaré sequence, consistent phrases, cusp kinds, finite dimensionality of the gap of automorphic different types of a given style, compactness of yes convolution operators, Eisenstein sequence, unitary representations of G, and the spectral decomposition of L2(^D*G/G). the most necessities are a few leads to useful research (reviewed, with references) and a few familiarity with the effortless idea of Lie teams and Lie algebras

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4 NPY and Adiposity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 NPY and Energy Expenditure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Problems with the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Potential Clinical Applications of NPY . . . . . . . . . . . . .

Woods Ammar and colleagues (Ammar et al. 2000) when they observed that NPY infusion could actually decrease food intake in some social situations. Using a different approach (Drazen et al. 2005), we found that rats trained to anticipate receiving NPY at a specific time of day learn to eat more at that time even when no NPY is administered. , there is compelling evidence that rather than initiating eating per se, NPY acts upon circuits that prepare and thus enable the animal to consume large meals.

7 Potential Clinical Applications of NPY . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 27 29 30 31 32 35 36 36 Abstract When administered into the brain, NPY acts at Y1 and Y5 receptors to increase food intake.

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Automorphic forms on SL₂(R) by Armand Borel


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