06180nam 22007332 450 991081754450332120160526163425.01-107-23372-01-139-60986-61-139-61172-01-139-62102-51-283-94313-11-139-62474-11-139-61544-01-139-60838-X1-139-04708-6(CKB)2670000000324853(EBL)1099818(OCoLC)823724583(SSID)ssj0000877947(PQKBManifestationID)11455184(PQKBTitleCode)TC0000877947(PQKBWorkID)10829083(PQKB)10183305(UkCbUP)CR9781139047081(Au-PeEL)EBL1099818(CaPaEBR)ebr10643422(CaONFJC)MIL425563(MiAaPQ)EBC1099818(PPN)261276271(EXLCZ)99267000000032485320110304d2013|||| uy| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierClassical and multilinear harmonic analysisVolume 1 /Camil Muscalu, Wilhelm Schlag[electronic resource]Cambridge :Cambridge University Press,2013.1 online resource (xviii, 370 pages) digital, PDF file(s)Cambridge studies in advanced mathematics ;137Title from publisher's bibliographic system (viewed on 05 Oct 2015).1-107-47159-1 0-521-88245-1 Includes bibliographical references and index.Contents; Preface; Acknowledgements; 1 Fourier series: convergence and summability; 1.1 The basics: partial sums and the Dirichlet kernel; 1.2 Approximate identities, Fej ́er kernel; 1.3 The Lp convergence of partial sums; 1.4 Regularity and Fourier series; 1.5 Higher dimensions; 1.6 Interpolation of operators; Notes; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; Problems; 2 Harmonic functions; Poisson kernel; 2.1 Harmonic functions; 2.2 The Poisson kernel; 2.3 The Hardy-Littlewood maximal function2.4 Almost everywhere convergence2.5 Weighted estimates for maximal functions; Notes; 3 Conjugate harmonic functions; Hilbert transform; 3.1 Hardy spaces of analytic functions; 3.2 Riesz theorems; 3.3 Definition and simple properties of the conjugate function; 3.4 The weak-L1 bound on the maximal function; 3.5 The Hilbert transform; 3.6 Convergence of Fourier series in Lp; Notes; 4 The Fourier transform on Rd and on LCA groups; 4.1 The Euclidean Fourier transform; 4.2 Method of stationary or nonstationary phases; 4.3 The Fourier transform on locally compact Abelian groups; Notes5 Introduction to probability theory5.1 Probability spaces; independence; 5.2 Sums of independent variables; 5.3 Conditional expectations; martingales; Notes; 6 Fourier series and randomness; 6.1 Fourier series on L1(T): pointwise questions; 6.2 Random Fourier series: the basics; 6.3 Sidon sets; Notes; 7 Calder ́on-Zygmund theory of singular integrals; 7.1 Calder ́on-Zygmund kernels; 7.2 The Laplacian: Riesz transforms and fractional integration; 7.3 Almost everywhere convergence; homogeneous kernels; 7.4 Bounded mean oscillation space; 7.5 Singular integrals and Ap weights7.6 A glimpse of H1-BMO duality and further remarksNotes; 8 Littlewood-Paley theory; 8.1 The Mikhlin multiplier theorem; 8.2 Littlewood-Paley square-function estimate; 8.3 Calderon-Zygmund H ̈older spaces, and Schauder estimates; 8.4 The Haar functions; dyadic harmonic analysis; 8.5 Oscillatory multipliers; Notes; 9 Almost orthogonality; 9.1 Cotlar's lemma; 9.2 Calderon-Vaillancourt theorem; 9.3 Hardy's inequality; 9.4 The T(1) theorem via Haar functions; 9.5 Carleson measures, BMO, and T(1); Notes; 10 The uncertainty principle; 10.1 Bernstein's bound and Heisenberg's uncertainty principle10.2 The Amrein-Berthier theorem10.3 The Logvinenko-Sereda theorem; 10.4 Solvability of constant-coefficient linear PDEs; Notes; 11 Fourier restriction and applications; 11.1 The Tomas-Stein theorem; 11.2 The endpoint; 11.3 Restriction and PDE; Strichartz estimates; 11.4 Optimal two-dimensional restriction; Notes; 12 Introduction to the Weyl calculus; 12.1 Motivation, definitions, basic properties; 12.2 Adjoints and compositions; 12.3 The L2 theory; 12.4 A phase-space transform; Notes; References; IndexThis two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón-Zygmund and Littlewood-Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman-Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.Cambridge studies in advanced mathematics ;137.Classical & Multilinear Harmonic AnalysisHarmonic analysisHarmonic analysis.515/.2422Muscalu Camil480408Schlag Wilhelm1969-UkCbUPUkCbUPBOOK9910817544503321Classical and multilinear harmonic analysis4003722UNINA04954nam 22007695 450 991030053320332120200704040607.03-319-78361-010.1007/978-3-319-78361-1(CKB)4100000004243856(DE-He213)978-3-319-78361-1(MiAaPQ)EBC6311848(PPN)227402936(EXLCZ)99410000000424385620180512d2018 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierLinear Algebra and Analytic Geometry for Physical Sciences /by Giovanni Landi, Alessandro Zampini1st ed. 2018.Cham :Springer International Publishing :Imprint: Springer,2018.1 online resource (XII, 345 p.) Undergraduate Lecture Notes in Physics,2192-47913-319-78360-2 Introduction -- Vectors and coordinate systems -- Vector spaces -- Euclidean vector spaces -- Matrices -- The determinant -- Systems of linear equations -- Linear transformations -- Dual spaces -- Endomorphisms and diagonalization -- Spectral theorems on euclidean spaces -- Rotations -- Spectral theorems on hermitian spaces -- Quadratic forms -- Affine linear geometry -- Euclidean affine linear geometry -- Conic sections -- A Algebraic Structures -- A.1 A few notions of Set Theory -- A.2 Groups -- A.3 Rings and Fields -- A.4 Maps between algebraic structures -- A5 Complex numbers -- A.6 Integers modulo a prime number.A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises. Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac’s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers modulo a prime number. The book will be useful to students taking a physics or engineer degree for a basic education as well as for students who wish to be competent in the subject and who may want to pursue a post-graduate qualification.Undergraduate Lecture Notes in Physics,2192-4791PhysicsMatrix theoryAlgebraApplied mathematicsEngineering mathematicsGeometryComputer science—MathematicsMathematical physicsMathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Linear and Multilinear Algebras, Matrix Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11094Mathematical and Computational Engineeringhttps://scigraph.springernature.com/ontologies/product-market-codes/T11006Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21006Math Applications in Computer Sciencehttps://scigraph.springernature.com/ontologies/product-market-codes/I17044Mathematical Applications in the Physical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13120Physics.Matrix theory.Algebra.Applied mathematics.Engineering mathematics.Geometry.Computer science—Mathematics.Mathematical physics.Mathematical Methods in Physics.Linear and Multilinear Algebras, Matrix Theory.Mathematical and Computational Engineering.Geometry.Math Applications in Computer Science.Mathematical Applications in the Physical Sciences.512.9Landi Giovanniauthttp://id.loc.gov/vocabulary/relators/aut61504Zampini Alessandroauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910300533203321Linear Algebra and Analytic Geometry for Physical Sciences2525355UNINA