TY - BOOK
AU - Unterberger,AndrĂ©
ED - SpringerLink (Online service)
TI - Alternative Pseudodifferential Analysis: With an Application to Modular Forms
T2 - Lecture Notes in Mathematics,
SN - 9783540779117
AV - QA370-380
U1 - 515.353 23
PY - 2008///
CY - Berlin, Heidelberg
PB - Springer Berlin Heidelberg, Imprint: Springer
KW - Differential equations, partial
KW - Topological Groups
KW - Fourier analysis
KW - Number theory
KW - Partial Differential Equations
KW - Topological Groups, Lie Groups
KW - Fourier Analysis
KW - Number Theory
N1 - Preface -- Introduction -- The Metaplectic and Anaplectic Representations -- The One-dimensional Alternative Pseudodifferential Analysis -- From Anaplectic Analysis to Usual Analysis -- Pseudodifferential Analysis and Modular Forms -- Index -- Bibliography
N2 - This volume introduces an entirely new pseudodifferential analysis on the line, the opposition of which to the usual (Weyl-type) analysis can be said to reflect that, in representation theory, between the representations from the discrete and from the (full, non-unitary) series, or that between modular forms of the holomorphic and substitute for the usual Moyal-type brackets. This pseudodifferential analysis relies on the one-dimensional case of the recently introduced anaplectic representation and analysis, a competitor of the metaplectic representation and usual analysis. Besides researchers and graduate students interested in pseudodifferential analysis and in modular forms, the book may also appeal to analysts and physicists, for its concepts making possible the transformation of creation-annihilation operators into automorphisms, simultaneously changing the usual scalar product into an indefinite but still non-degenerate one
UR - https://doi.org/10.1007/978-3-540-77911-7
ER -