01463nam0 2200349 450 00003687620141120151241.03-519-01399-120140620d1971----km-y0itaa50------bagrcDEHephaestionis Enchiridion cum commentariis veteribusedidit Maximilian ConsbruchEditio stereotypa editionis anni 1906Stutgardiaein aedibus B. G. Teubneri1971XXXII, 430 p.21 cmBibliotheca scriptorum Graecorum et Romanorum TeubnerianaAccedunt variae metricorum Graecorum reliquiae2001Bibliotheca scriptorum Graecorum et Romanorum TeubnerianaEnchiridion de metris / Hephaestion27420486(22. ed.)Lingua greca. Prosodia, metricaHephaestion<2. saec.>290424Consbruch,MaximilianITUniversità della Basilicata - B.I.A.REICATunimarc000036876Enchiridion de metris27420UNIBASEXT0130120140620BAS010807EXT0130120140620BAS010812EXT0130120140620BAS010820EXT0130120141120BAS011512BAS01BAS01BOOKBASA1Polo Storico-UmanisticoGENCollezione generaleClass/149078334L783342014062002Prestabile GeneraleAccedunt variae metricorum Graecorum reliquiae01429nam0 2200313 450 00003783320140807122416.084-7317-130-620140807d1983----km-y0itaa50------baspaESDiálogo sobre la educación del Príncipe Don Juan, hijo de los Reyes Católicostexto traducido íntegramente al español del latín original, acompañado de algunas fotografíasAlonso Ortiz (S. XV-XVI)versión, notas e interpretaciones por Giovanni Maria BertiniMadrid<<José>> Porrúa TuranzasPotomac (Maryland)Studia humanitatis1983VIII, 249 p., 8 p. di tav.ill.22 cmStudia humanitatis2001Studia humanitatisAragón,Juan deComportamento860.2(22. ed.)Letteratura spagnola. 1369-1516Ortiz,Alonso447202Bertini,Giovanni MariaITUniversità della Basilicata - B.I.A.REICATunimarc000037833Diálogo sobre la educación del Príncipe Don Juan, hijo de los Reyes Católicos1530227UNIBASLETTEREEXT0170120140807BAS011222EXT0170120140807BAS011224BAS01BAS01BOOKBASA1Polo Storico-UmanisticoDSLFCollezione DiSLFDF/E8781880F18802014080704Prestabile Didattica05944nam 2200577 450 99648317250331620230727185456.03-031-06186-1(MiAaPQ)EBC7052885(Au-PeEL)EBL7052885(CKB)24286234000041(PPN)263897001(EXLCZ)992428623400004120230106d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierWave packet analysis of Feynman path integrals /Fabio Nicola, S. Ivan TrapassoCham, Switzerland :Springer,[2022]©20221 online resource (220 pages)Lecture notes in mathematics ;Volume 2305Print version: Nicola, Fabio Wave Packet Analysis of Feynman Path Integrals Cham : Springer International Publishing AG,c2022 9783031061851 Includes bibliographical references and index.Intro -- Preface -- Contents -- Outline -- 1 Itinerary: How Gabor Analysis Met Feynman Path Integrals -- 1.1 The Elements of Gabor Analysis -- 1.1.1 The Analysis of Functions via Gabor Wave Packets -- 1.2 The Analysis of Operators via Gabor Wave Packets -- 1.2.1 The Problem of Quantization -- 1.2.2 Metaplectic Operators -- 1.3 The Problem of Feynman Path Integrals -- 1.3.1 Rigorous Time-Slicing Approximation of Feynman Path Integrals -- 1.3.2 Pointwise Convergence at the Level of Integral Kernels for Feynman-Trotter Parametrices -- 1.3.3 Convergence of Time-Slicing Approximations in L(L2) for Low-Regular Potentials -- 1.3.4 Convergence of Time-Slicing Approximations in the Lp Setting -- Part I Elements of Gabor Analysis -- 2 Basic Facts of Classical Analysis -- 2.1 General Notation -- 2.2 Function Spaces -- 2.2.1 Lebesgue Spaces -- 2.2.2 Differentiable Functions and Distributions -- 2.3 Basic Operations on Functions and Distributions -- 2.4 The Fourier Transform -- 2.4.1 Convolution and Fourier Multipliers -- 2.5 Some More Facts and Notations -- 3 The Gabor Analysis of Functions -- 3.1 Time-Frequency Representations -- 3.1.1 The Short-Time Fourier Transform -- 3.1.2 Quadratic Representations -- 3.2 Modulation Spaces -- 3.3 Wiener Amalgam Spaces -- 3.4 A Banach-Gelfand Triple of Modulation Spaces -- 3.5 The Sjöstrand Class and Related Spaces -- 3.6 Complements -- 3.6.1 Weight Functions -- 3.6.2 The Cohen Class of Time-Frequency Representations -- 3.6.3 Kato-Sobolev Spaces -- 3.6.4 Fourier Multipliers -- 3.6.5 More on the Sjöstrand Class -- 3.6.6 Boundedness of Time-Frequency Transforms on Modulation Spaces -- 3.6.7 Gabor Frames -- 4 The Gabor Analysis of Operators -- 4.1 The General Program -- 4.2 The Weyl Quantization -- 4.3 Metaplectic Operators -- 4.3.1 Notable Facts on Symplectic Matrices.4.3.2 Metaplectic Operators: Definitions and Basic Properties -- 4.3.3 The Schrödinger Equation with Quadratic Hamiltonian -- 4.3.4 Symplectic Covariance of the Weyl Calculus -- 4.3.5 Gabor Matrix of Metaplectic Operators -- 4.4 Fourier and Oscillatory Integral Operators -- 4.4.1 Canonical Transformations and the Associated Operators -- 4.4.2 Generalized Metaplectic Operators -- 4.4.3 Oscillatory Integral Operators with Rough Amplitude -- 4.5 Complements -- 4.5.1 Weyl Operators and Narrow Convergence -- 4.5.2 General Quantization Rules -- 4.5.3 The Class FIO'(S,vs) -- 4.5.4 Finer Aspects of Gabor Wave Packet Analysis -- 5 Semiclassical Gabor Analysis -- 5.1 Semiclassical Transforms and Function Spaces -- 5.1.1 Sobolev Spaces and Embeddings -- 5.2 Semiclassical Quantization, Metaplectic Operators and FIOs -- Part II Analysis of Feynman Path Integrals -- 6 Pointwise Convergence of the Integral Kernels -- 6.1 Summary -- 6.2 Preliminary Results -- 6.2.1 The Schwartz Kernel Theorem -- 6.2.2 Uniform Estimates for Linear Changes of Variable -- 6.2.3 Exponentiation in Banach Algebras -- 6.2.4 Two Technical Lemmas -- 6.3 Reduction to the Case .12em.1emdotteddotteddotted.76dotted.6h=(2π)-1 -- 6.4 The Fundamental Solution and the Trotter Formula -- 6.5 Potentials in M∞0,s -- 6.6 Potentials in C∞b -- 6.7 Potentials in the Sjöstrand Class M∞,1 -- 6.8 Convergence at Exceptional Times -- 6.9 Physics at Exceptional Times -- 7 Convergence in L(L2) for Potentials in the Sjöstrand Class -- 7.1 Summary -- 7.2 An Abstract Approximation Result in L(L2) -- 7.3 Short-Time Analysis of the Action -- 7.4 Estimates for the Parametrix and Convergence Results -- 8 Convergence in L(L2) for Potentials in Kato-Sobolev Spaces -- 8.1 Summary -- 8.2 Sobolev Regularity of the Hamiltonian Flow -- 8.3 Sobolev Regularity of the Classical Action.8.4 Analysis of the Parametrices and Convergence Results -- 8.5 Higher-Order Parametrices -- 9 Convergence in the Lp Setting -- 9.1 Summary -- 9.2 Review of the Short Time Analysis in the Smooth Category -- 9.3 Wave Packet Analysis of the Schrödinger Flow -- 9.4 Convergence in Lp with Loss of Derivatives -- 9.5 The Case of Magnetic Fields -- 9.6 Sharpness of the Results -- 9.7 Extensions to the Case of Rough Potentials -- Bibliography -- Index.Lecture notes in mathematics (Springer-Verlag) ;Volume 2305.Feynman integralsGabor transformsQuantum theoryIntegrals de FeynmanthubTeoria quànticathubLlibres electrònicsthubFeynman integrals.Gabor transforms.Quantum theory.Integrals de FeynmanTeoria quàntica515.43Nicola Fabio1252174Trapasso S. IvanMiAaPQMiAaPQMiAaPQBOOK996483172503316Wave packet analysis of Feynman path integrals2999685UNISA