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Produktbild: Analysis of Divergence
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Analysis of Divergence Control and Management of Divergent Processes

Aus der Reihe Applied and Numerical Harmonic Analysis
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83,99 € UVP 96,29 €

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

01.11.1998

Herausgeber

William Bray + weitere

Verlag

Birkhäuser Boston

Seitenzahl

568

Maße (L/B/H)

24,2/16,5/3,1 cm

Gewicht

971 g

Auflage

1999 edition

Sprache

Englisch

ISBN

978-0-8176-4058-3

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

01.11.1998

Herausgeber

Verlag

Birkhäuser Boston

Seitenzahl

568

Maße (L/B/H)

24,2/16,5/3,1 cm

Gewicht

971 g

Auflage

1999 edition

Sprache

Englisch

ISBN

978-0-8176-4058-3

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Analysis of Divergence
  • Overview.- I Convergence and Summability.- 1 Tauberian theorems for generalized Abelian summability methods.- 1.1 Introduction.- 1.2 A General Summability Method.- 1.3 Generalized Abel’s Summability Methods.- 2 Series summability of complete biorthogonal sequences.- 2.1 Introduction.- 2.2 Preliminaries.- 2.2.1 Biorthogonal Sequences.- 2.2.2 Sequence Spaces.- 2.2.3 The Beta-Phi Topology on a Sequence Space.- 2.2.4 Biorthogonal Sequences and Sequence Spaces.- 2.2.5 Multiplier Algebras, Sums, and Sum Spaces.- 2.2.6 Convergence Properties of Sequence Spaces.- 2.3 Sums and Sum Spaces.- 2.3.1 Sums.- 2.3.2 Sum Spaces.- 2.4 Inclusion Theorems.- 3 Growth of Cesàro means of double Vilenkin-Fourier series of unbounded type.- 3.1 Introduction.- 3.2 Fundamental concepts and notation.- 3.3 The Vilenkin-Fejér kernel.- 3.4 The main results.- 4 A substitute for summability in wavelet expansions.- 4.1 Introduction.- 4.2 Background.- 4.3 Summability for Wavelets With Compact Support.- 4.4 The Properties Of The Summability Function.- 4.4.1 The rate of decrease of the filter coefficients.- 4.4.2 The calculation of the positive estimation
    $$f^r_m(t)$$.- 5 Expansions in series of Legendre functions.- 5.1 Introduction.- 5.2 Preliminaries and known results.- 5.2.1 Christoffel Summation Formula.- 5.2.2 Stieltjes’s Inequality.- 5.2.3 Riemann-Lebesgue-type Theorem.- 5.2.4 Singular Integrals.- 5.3 Neumann’s Integral and consequences.- 5.4 Hunter’s Identities.- 6 Endpoint convergence of Legendre series.- 6.1 Statement of results.- 6.2 Asymptotic estimates.- 6.3 Convergence at the endpoints.- 6.3.1 Convergence at x = 1.- 6.3.2 Convergence at x = -1.- 7 Inversion of the horocycle transform on real hyperbolic spaces via a wavelet-like transform.- 7.1 Introduction.- 7.2 Preliminaries.- 7.2.1 Algebraic and geometric notions.- 7.2.2 The horocycle transform and its dual.- 7.2.3 Approximate identities on ?.- 7.3 Inversion of the Horocycle Transform.- 8 Fourier-Bessel expansions with general boundary conditions.- 8.1 Introduction.- 8.2 Statement of Results.- 8.3 Proofs.- 8.4 Identifying the limit.- 8.4.1 An Abelian lemma.- II Singular Integrals and Multipliers.- 9 Convolution Calderón-Zygmund singular integral operators with rough kernels.- 9.1 Introduction.- 9.2 L2 boundedness.- 9.3 Lp boundedness, 1 < p < ?.- 9.4 The L1 theory.- 9.5 Another H1 condition in dimension 2.- 9.6 Maximal functions and maximal singular integrals.- 10 Haar multipliers, paraproducts, and weighted inequalities.- 10.1 Introduction.- 10.2 Preliminaries.- 10.2.1 Dyadic intervals and Haar basis.- 10.2.2 Weights.- 10.3 Weight lemma and decaying stopping times.- 10.4 Lp Lemmas for decaying stopping times.- 10.4.1 Lp Plancherel Lemma.- 10.4.2 Lp version of Cotlar’s Lemma.- 10.5 Boundedness of
    $$
    T_\omega ^t
    $$.- 10.5.1 Boundedness of T?.- 10.5.2 Some corollaries.- 10.6 Haar multipliers and weighted inequalities.- 11 Multipliers and square functions for Hp spaces over Vilenkin groups.- 11.1 Introduction.- 11.2 Historical Comments.- 11.3 Multipliers for Hp (0 for oscillatory Fourier transforms.- 14.1 Introduction.- 14.2 Lp(L?)-estimates.- 14.3 L2(L2)-estimates.- 15 Optimal spaces for the S’-convolution with the Marcel Riesz kernels and the N-dimensional Hilbert kernel.- 15.1 Introduction.- 15.2 Definitions and notation.- 15.2.1 Function and distribution spaces.- 15.2.2 The S’-convolution.- 15.2.3 Partition of unity on
    $$\mathbb{R}^n$$.- 15.3 Optimal space for the S’-convolution with the vector Riesz kernel.- 15.4 Optimal space for the S’-convolution with
    $$p\nu \frac{1}{x_1} \otimes \cdots \otimes p\nu \frac{1}{x_n}$$.- 15.5 Necessary condition for the S’-convolvability with a single Riesz kernel.- III Integral Operators and Functional Analysis.- 16 Asymptotic expansions and linear wavelet packets on certain hypergroups.- 16.1 Introduction.- 16.2 The Chébli-Trimèche hypergroups
    $$(\mathbb{R}_+,*_A)$$.- 16.3 The dual of the hypergroups
    $$(\mathbb{R}_+,*_A)$$.- 16.4 Asymptotic expansions and integral representations of Mehler and Schläfli type.- 16.4.1 The asymptotic expansions.- 16.4.2 Integral representations of Mehler and Schläfli type.- 16.5 Harmonic analysis and maximal ideal spaces of some algebras.- 16.5.1 Harmonic analysis.- 16.5.2 The maximal ideal spaces of the algebras and
    $$
    L^1 (m_A )\;\text{and}\;M_b (\text{R}_ + )
    $$.- 16.6 Continuous linear wavelet transform and its discretization.- 16.6.1 Linear wavelets on
    $$(\mathbb{R}_+,*_A)$$.- 16.6.2 Linear wavelet packet on
    $$(\mathbb{R}_+,*_A)$$.- 16.6.3 Scale discrete L-scaling function on
    $$(\mathbb{R}_+,*_A)$$.- 17 Hardy-type inequalities for a new class of integral operators.- 17.1 Introduction.- 17.2 Starshaped regions.- 17.3 Prom regions to kernels.- 18 Regularly bounded functions and Hardy’s inequality.- 18.1 Introduction.- 18.2 Definition and Uniform Boundedness.- 18.3 The global bounds.- 18.4 The representation theorem.- 18.5 The multiplicative class.- 18.6 Abelian Theorems.- 18.7 Hardy’s Inequality.- 19 Extremal problems in generalized Sobolev classes.- 19.1 Introduction.- 19.1.1 General problem of sharp inequalities for intermediate derivatives.- 19.1.2 Functional classes
    $$W^rH^\omega(\mathbb{I})$$.- 19.1.3 The Kolmogorov problem in
    $$W^rH^\omega(\mathbb{I})$$.- 19.2 Maximization of integral functional over H?[a, b].- 19.2.1 Simple kernels ?(·) and their rearrangements
    $$
    \Re (\Psi \text{;} \cdot )
    $$.- 19.2.2 The Korneichuk lemma.- 19.2.3 Extremal functions of functionals over H?[a, b].- 19.2.4 Structural properties of extremal functions
    $$
    x_{\omega ,\psi }
    $$.- 19.3 Kolmogorov problem for intermediate derivatives.- 19.3.1 Differentiation formulae for f(m)(0), 0 ? m < r.- 19.3.2 Differentiation formula for f(r)(0).- 19.3.3 Sufficient conditions of extremality.- 19.3.4 Extremaiity conditions in the form of an operator equation.- 19.3.5 Sharp additive inequalities for intermediate derivatives.- 19.3.6 Kolmogorov problem in Hölder classes.- 19.4 Kolmogorov problem in
    $$W^1H^\omega(\mathbb{R}_+)$$
    and
    $$W^1H^\omega(\mathbb{R}_+)$$.- 19.4.1 Preliminary remarks.- 19.4.2 Maximization of the norm
    $$\Vert f \Vert L_{\infty}(\mathbb{R}_+)$$.- 19.4.3 Extremal functions in Hölder classes $${{\rm H}^\omega }[a,b]$$.- 19.4.4 Maximization of the norm
    $$\Vert f^\prime \Vert L_{\infty}(\mathbb{R}_+)$$.- 19.4.5 Maximization of the norm
    $$\Vert f \Vert L_{\infty}(\mathbb{R}_+)$$.- 19.4.6 Maximization of the norm
    $$\Vert f^\prime \Vert L_{\infty}(\mathbb{R}_+)$$.- 20 On angularly perturbed Laplace equations in the unit ball and their distributional boundary values.- 20.1 Introduction.- 20.2 Notation and Preliminaries.- 20.3 Bounded Solutions on Bn+2.- 20.4 Distributional Boundary Values.- 20.5 Generalities.- 21 Nonresonant semilinear equations and applications to boundary value problems.- 21.1 Introduction.- 21.2 Semi-abstract nonresonance problems.- 21.3 Strong solvability of elliptic BVP’s.- 21.4 Time periodic solutions of BVP’s for nonlinear parabolic and hyperbolic equations.- 21.4.1 Nonlinear parabolic equations.- 21.4.2 Applications to the heat equation.- 21.4.3 Nonlinear hyperbolic equtions.- 21.4.4 Applications to the telegraph equation.- 21.4.5 Application to the beam equation with damping.- 22 A topological and functional analytic approach to statistical convergence.- 22.1 Introduction.- 22.2 The support set of a measure.- 22.3 Invariants of statistical convergence.- 22.4 Summability theorems.- IV Asymptotics and Applications.- 23 Optimal control of divergent control systems.- 23.1 Introduction and History.- 23.2 Basic models and hypotheses.- 23.3 Existence of optimal solutions.- 23.3.1 Existence of overtaking optimal solutions without discounting.- 23.3.2 Existence of overtaking optimal solutions with discounting.- 23.4 The associated uncoupled optimal control problems.- 23.4.1 The undiscounted case.- 23.4.2 The discounted case.- 23.5 Optimal solutions of the explicitly state constrained optimal control problem.- 23.5.1 The undiscounted case.- 23.6 Conclusions.- 24 Surfaces minimizing integrals of divergent integrands.- 24.1 Introduction.- 24.2 Surfaces and Integrands.- 24.3 Overtaking Minimizers.- 24.4 A Radially Symmetric Example.- 24.5 Hypotheses for Regularity.- 24.6 Barriers.- 24.7 A Result in Differential Geometry.- 24.8 Bounding the Curvature.- 25 Sparse exponential sums with low sidelobes.- 25.1 Introduction.- 25.2 Generalized Rudin-Shapiro Polynomials.- 25.3 Exponential Sums with Low Sidelobes.- 26 Spline type summability for multivariate sampling.- 26.1 Introduction.- 26.1.1 Sampling theory.- 26.1.2 Splines and sampling theory.- 26.1.3 Contents, notation, and acknowledgements.- 26.2 Regular sampling of multivariate functions and their recovery via splines.- 26.2.1 Band limited functions and polyharmonic splines.- 26.2.2 The spaces
    $$L^{2,k}(\mathbb{R}^n)$$
    and
    $$L^{2,k}(\mathbb{Z}^n)$$
    and the variational properties of polyharmonic splines.- 26.2.3 The Paley-Wiener space
    $$PW^k_\pi$$.- 26.2.4 Convergence of m-harmonic splines as m ? ?.- 26.3 Generalizations, related methods, and computational issues.- 26.3.1 Generalizations.- 26.3.2 Multivariate analogues of the Paley-Wiener Theorem and the sampling theorem.- 26.3.3 Box splines.- 26.3.4 Computing polyharmonic splines.- 27 B-Splines and orthonormal sets in Paley-Wiener space.- 27.1 Introduction.- 27.2 Preliminaries.- 27.3 Sampling and Orthonormal Functions.- 27.4 B-splines and Orthonormal Sets in the Paley-Wiener Space.- 28 Norms of powers and a central limit theorem.- 28.1 Introduction.- 28.2 The Five Parameters.- 28.3 Boundedness.- 28.3.1 Power Series.- 28.3.2 Trigonometric Series.- 28.4 Asymptotic Behavior.- 28.5 Asymptotic Series.- 28.6 Changing the Question.- 28.7 Behavior of Scaled ?(n) for Large n.- 28.8 Another Kind of Central Limit Theorems.- 29 Quasiasymptotics at zero and nonlinear problems in a framework of Colombeau generalized functions.- 29.1 Introduction.- 29.2 Algebra of generalized functions.- 29.3 G-quasiasymptotics at zero.- 29.4 Application of G quasiasymptotics to generalized solutions.- 29.4.1 System of nonlinear Volterra integral equations with non-Lipschitz nonlinearity.- 29.4.2 Semilinear hyperbolic system.- 29.4.3 Nonlinear wave equation.- 29.4.4 Euler-Lagrange equation.- 29.4.5 Goursat problem.