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035   $a(OCoLC)979633761
035   $a(DE-B1597)9781400882427
035   $a(iGPub)PUPB0005391
035   $a(EXLCZ)993710000000620149
100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aHarmonic Analysis in Phase Space. (AM-122), Volume 122 /$fGerald B. Folland
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$d©1989
215   $a1 online resource (289 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v353
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08527-7 
311   $a0-691-08528-5 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tCONTENTS -- $tPREFACE -- $tPROLOGUE. SOME MATTERS OF NOTATION -- $tCHAPTER 1. THE HEISENBERG GROUP AND ITS REPRESENTATIONS -- $tCHAPTER 2. QUANTIZATION AND PSEUDODIFFERENTIAL OPERATORS -- $tCHAPTER 3. WAVE PACKETS AND WAVE FRONTS -- $tCHAPTER 4. THE METAPLECTIC REPRESENTATION -- $tCHAPTER 5. THE OSCILLATOR SEMIGROUP -- $tAPPENDIX A. GAUSSIAN INTEGRALS AND A LEMMA ON DETERMINANTS -- $tAPPENDIX B. SOME HILBERT SPACE RESULTS -- $tBIBLIOGRAPHY -- $tINDEX
330   $aThis book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.
410  0$aAnnals of mathematics studies ;$vno. 122.
606   $aPhase space (Statistical physics)
606   $aHarmonic analysis
610   $aAnalytic continuation.
610   $aAnalytic function.
610   $aAntisymmetric tensor.
610   $aAsymptotic expansion.
610   $aAutomorphism.
610   $aBilinear form.
610   $aBounded operator.
610   $aCalculation.
610   $aCanonical commutation relation.
610   $aCanonical transformation.
610   $aCauchy?Riemann equations.
610   $aCayley transform.
610   $aClass function (algebra).
610   $aClassical mechanics.
610   $aCommutative property.
610   $aComplex analysis.
610   $aConfiguration space.
610   $aDifferential equation.
610   $aDifferential geometry.
610   $aDifferential operator.
610   $aEigenvalues and eigenvectors.
610   $aEquation.
610   $aExplicit formula.
610   $aFock space.
610   $aFourier analysis.
610   $aFourier integral operator.
610   $aFourier transform.
610   $aFunctional analysis.
610   $aGaussian function.
610   $aGaussian integral.
610   $aGeometric quantization.
610   $aHamiltonian mechanics.
610   $aHamiltonian vector field.
610   $aHarmonic analysis.
610   $aHeisenberg group.
610   $aHermite polynomials.
610   $aHermitian symmetric space.
610   $aHilbert space.
610   $aHilbert transform.
610   $aIntegral transform.
610   $aInvariant subspace.
610   $aIrreducible representation.
610   $aLebesgue measure.
610   $aLie algebra.
610   $aLie superalgebra.
610   $aLie theory.
610   $aMathematical physics.
610   $aNumber theory.
610   $aObservable.
610   $aOrdinary differential equation.
610   $aOrthonormal basis.
610   $aOscillator representation.
610   $aOscillatory integral.
610   $aPartial differential equation.
610   $aPhase factor.
610   $aPhase space.
610   $aPoint at infinity.
610   $aPoisson bracket.
610   $aPolynomial.
610   $aPower series.
610   $aProbability.
610   $aProjection (linear algebra).
610   $aProjective Hilbert space.
610   $aProjective representation.
610   $aProjective space.
610   $aPseudo-differential operator.
610   $aPullback (category theory).
610   $aQuadratic function.
610   $aQuantum harmonic oscillator.
610   $aQuantum mechanics.
610   $aRepresentation theory.
610   $aSchrödinger equation.
610   $aSelf-adjoint operator.
610   $aSemigroup.
610   $aSeveral complex variables.
610   $aSiegel disc.
610   $aSobolev space.
610   $aSpectral theorem.
610   $aSpectral theory.
610   $aState-space representation.
610   $aStone's theorem.
610   $aStone?Weierstrass theorem.
610   $aSummation.
610   $aSymmetric space.
610   $aSymmetric tensor.
610   $aSymplectic geometry.
610   $aSymplectic group.
610   $aSymplectic vector space.
610   $aSymplectomorphism.
610   $aTangent space.
610   $aTangent vector.
610   $aTheorem.
610   $aTranslational symmetry.
610   $aUnbounded operator.
610   $aUnit vector.
610   $aUnitarity (physics).
610   $aUnitary operator.
610   $aUnitary representation.
610   $aVariable (mathematics).
610   $aWave packet.
615  0$aPhase space (Statistical physics)
615  0$aHarmonic analysis.
676   $a530.1/3
700   $aFolland$b Gerald B., $041512
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154752303321
996   $aHarmonic Analysis in Phase Space. (AM-122), Volume 122$92670337
997   $aUNINA