LEADER 05555nam 22007334a 450 001 9911019370403321 005 20200520144314.0 010 $a9786610242771 010 $a9781280242779 010 $a1280242779 010 $a9780470022733 010 $a0470022736 010 $a9780470022726 010 $a0470022728 035 $a(CKB)1000000000357216 035 $a(EBL)241159 035 $a(SSID)ssj0000095719 035 $a(PQKBManifestationID)11515892 035 $a(PQKBTitleCode)TC0000095719 035 $a(PQKBWorkID)10075957 035 $a(PQKB)10752020 035 $a(MiAaPQ)EBC241159 035 $a(OCoLC)85820706 035 $a(Perlego)2748971 035 $a(EXLCZ)991000000000357216 100 $a20050624d2005 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$a3D videocommunication $ealgorithms, concepts, and real-time systems in human centred communication /$fedited by Oliver Schreer, Peter Kauff, Thomas Sikora 210 $aChichester, England ;$aHoboken, NJ $cWiley$d2005 215 $a1 online resource (366 p.) 300 $aDescription based upon print version of record. 311 08$a9780470022719 311 08$a047002271X 320 $aIncludes bibliographical references and index. 327 $a3D Videocommunication; Contents; List of Contributors; Symbols; Abbreviations; Introduction; Section I Applications of 3D Videocommunication; 1 History of Telepresence; 1.1 Introduction; 1.2 The Art of Immersion: Barker's Panoramas; 1.3 Cinerama and Sensorama; 1.4 Virtual Environments; 1.5 Teleoperation and Telerobotics; 1.6 Telecommunications; 1.7 Conclusion; References; 2 3D TV Broadcasting; 2.1 Introduction; 2.2 History of 3D TV Research; 2.3 A Modern Approach to 3D TV; 2.3.1 A Comparison with a Stereoscopic Video Chain; 2.4 Stereoscopic View Synthesis; 2.4.1 3D Image Warping 327 $a2.4.2 A 'Virtual' Stereo Camera2.4.3 The Disocclusion Problem; 2.5 Coding of 3D Imagery; 2.5.1 Human Factor Experiments; 2.6 Conclusions; Acknowledgements; References; 3 3D in Content Creation and Post-production; 3.1 Introduction; 3.2 Current Techniques for Integrating Real and Virtual Scene Content; 3.3 Generation of 3D Models of Dynamic Scenes; 3.4 Implementation of a Bidirectional Interface Between Real and Virtual Scenes; 3.4.1 Head Tracking; 3.4.2 View-dependent Rendering; 3.4.3 Mask Generation; 3.4.4 Texturing; 3.4.5 Collision Detection; 3.5 Conclusions; References 327 $a4 Free Viewpoint Systems4.1 General Overview of Free Viewpoint Systems; 4.2 Image Domain System; 4.2.1 EyeVision; 4.2.2 3D-TV; 4.2.3 Free Viewpoint Play; 4.3 Ray-space System; 4.3.1 FTV (Free Viewpoint TV); 4.3.2 Bird's-eye View System; 4.3.3 Light Field Video Camera System; 4.4 Surface Light Field System; 4.5 Model-based System; 4.5.1 3D Room; 4.5.2 3D Video; 4.5.3 Multi-texturing; 4.6 Integral Photography System; 4.6.1 NHK System; 4.6.2 1D-II 3D Display System; 4.7 Summary; References; 5 Immersive Videoconferencing; 5.1 Introduction; 5.2 The Meaning of Telepresence in Videoconferencing 327 $a5.3 Multi-party Communication Using the Shared Table Concept5.4 Experimental Systems for Immersive Videoconferencing; 5.5 Perspective and Trends; Acknowledgements; References; Section II 3D Data Representation and Processing; 6 Fundamentals of Multiple-view Geometry; 6.1 Introduction; 6.2 Pinhole Camera Geometry; 6.3 Two-view Geometry; 6.3.1 Introduction; 6.3.2 Epipolar Geometry; 6.3.3 Rectification; 6.3.4 3D Reconstruction; 6.4 N-view Geometry; 6.4.1 Trifocal Geometry; 6.4.2 The Trifocal Tensor; 6.4.3 Multiple-view Constraints; 6.4.4 Uncalibrated Reconstruction from N views 327 $a6.4.5 Autocalibration6.5 Summary; References; 7 Stereo Analysis; 7.1 Stereo Analysis Using Two Cameras; 7.1.1 Standard Area-based Stereo Analysis; 7.1.2 Fast Real-time Approaches; 7.1.3 Post-processing; 7.2 Disparity From Three or More Cameras; 7.2.1 Two-camera versus Three-camera Disparity; 7.2.2 Correspondence Search with Three Views; 7.2.3 Post-processing; 7.3 Conclusion; References; 8 Reconstruction of Volumetric 3D Models; 8.1 Introduction; 8.2 Shape-from-Silhouette; 8.2.1 Rendering of Volumetric Models; 8.2.2 Octree Representation of Voxel Volumes 327 $a8.2.3 Camera Calibration from Silhouettes 330 $aThe migration of immersive media towards telecommunication applications is advancing rapidly. Impressive progress in the field of media compression, media representation, and the larger and ever increasing bandwidth available to the customer, will foster the introduction of these services in the future. One of the key components for the envisioned applications is the development from two-dimensional towards three-dimensional audio-visual communications. With contributions from key experts in the field, 3D Videocommunication:provides a complete overview of existing systems and 606 $aTelematics 606 $aThree-dimensional imaging 606 $aVideoconferencing 606 $aVirtual reality 615 0$aTelematics. 615 0$aThree-dimensional imaging. 615 0$aVideoconferencing. 615 0$aVirtual reality. 676 $a006.7 701 $aSchreer$b Oliver$0863241 701 $aKauff$b Peter$01838090 701 $aSikora$b Thomas$01837671 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019370403321 996 $a3D videocommunication$94417003 997 $aUNINA LEADER 07604nam 22006015 450 001 9910585774903321 005 20251113204032.0 010 $a3-031-06186-1 024 7 $a10.1007/978-3-031-06186-8 035 $a(MiAaPQ)EBC7052885 035 $a(Au-PeEL)EBL7052885 035 $a(CKB)24286234000041 035 $a(PPN)263897001 035 $a(OCoLC)1337856497 035 $a(DE-He213)978-3-031-06186-8 035 $a(EXLCZ)9924286234000041 100 $a20220728d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aWave Packet Analysis of Feynman Path Integrals /$fby Fabio Nicola, S. Ivan Trapasso 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (220 pages) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v2305 311 08$aPrint version: Nicola, Fabio Wave Packet Analysis of Feynman Path Integrals Cham : Springer International Publishing AG,c2022 9783031061851 320 $aIncludes bibliographical references and index. 327 $aIntro -- 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. 327 $a4.3.2 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=(2?)-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. 327 $a8.4 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. 330 $aThe purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets ? can be successfully applied to mathematical path integrals, leading to remarkable results and paving the wayto a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v2305 606 $aQuantum theory 606 $aFunctional analysis 606 $aQuantum Physics 606 $aFunctional Analysis 615 0$aQuantum theory. 615 0$aFunctional analysis. 615 14$aQuantum Physics. 615 24$aFunctional Analysis. 676 $a515.43 676 $a530.1430151543 700 $aNicola$b Fabio$01252174 702 $aTrapasso$b S. Ivan 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910585774903321 996 $aWave packet analysis of Feynman path integrals$92999685 997 $aUNINA