Topic
Volume integral
About: Volume integral is a research topic. Over the lifetime, 3931 publications have been published within this topic receiving 110135 citations.
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Book•
08 Dec 1993
TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.
Abstract: Fractional integrals and derivatives on an interval fractional integrals and derivatives on the real axis and half-axis further properties of fractional integrals and derivatives other forms of fractional integrals and derivatives fractional integrodifferentiation of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations fo the first kind with special function kernels applications to differential equations.
7,096 citations
Book•
01 Jan 2002
TL;DR: In this article, the authors introduce the Heisenberg group and describe the Maximal Operators and Maximal Averages and Oscillatory Integral Integrals of the First and Second Kind.
Abstract: PrefaceGuide to the ReaderPrologue3IReal-Variable Theory7IIMore About Maximal Functions49IIIHardy Spaces87IVH[superscript 1] and BMO139VWeighted Inequalities193VIPseudo-Differential and Singular Integral Operators: Fourier Transform228VIIPseudo-Differential and Singular Integral Operators: Almost Orthogonality269VIIIOscillatory Integrals of the First Kind329IXOscillatory Integrals of the Second Kind375XMaximal Operators: Some Examples433XIMaximal Averages and Oscillatory Integrals467XIIIntroduction to the Heisenberg Group527XIIIMore About the Heisenberg Group587Bibliography645Author Index679Subject Index685
6,639 citations
2,090 citations
Book•
27 Dec 2005
TL;DR: In this paper, the authors present a list of applications of the path integral formula in statistical mechanics, including the application of the Path Integral formula to Statistical Mechanics, asymptotic analysis, and the phase space path integral.
Abstract: Partial table of contents: Probabilities and Probability Amplitudes for Paths. Correspondence Limit for the Path Integral (Heuristic). Vector Potentials and Another Proof of the Path Integral Formula. Doing the Integral: Free Particle and Quadratic Lagrangians. Brownian Motion and the Wiener Integral Kac's Proof. Perturbation Theory and Feynman Diagrams. SELECTED APPLICATIONS OF THE PATH INTEGRAL. Asymptotic Analysis. The Calculus of Variations. WKB Near Caustics. The Phase of the Semiclassical Amplitude. Scattering Theory. Geometrical Optics. The Polaron. Spin and Related Matters. Quantum Mechanics on Curved Spaces. Relativistic Propagators and Black Holes. Applications to Statistical Mechanics. Critical Droplets. Alias Instantons, and Metastability. Phase Space Path Integral. Omissions, Miscellany, and Prejudices. Indexes.
2,079 citations