Topic
Integral element
About: Integral element is a research topic. Over the lifetime, 482 publications have been published within this topic receiving 8041 citations.
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Papers
Book•
11 Nov 2010
TL;DR: The Radon Transformon on Rn 1.1-2-3-4-5-6-7-8-9-10-11-12-13-14-15-16-17-18-19-20-21-22-23-24-25-26-27-28-29-30-31-34-35-36-37-39-40-41-42-43-44-45-46-47-48-49-50-51-52-53-54-55-56-
Abstract: 1.- The Radon Transformon on Rn 1.1- Introduction 1.2- The Radon Transform: The Support Theorem 1.3- The Inversion Formula: Injectivity Questions 1.4- The Plancherel Formula 1.5- Radon Transform of Distribution 1.6- Integration over d-planes: X-Ray Transforms 1.7- Applications 2.- A Duality in Integral Geometry 2.1- Homogeneous Spaces in Duality 2.2- The Radon Transform for the Double Fibration: Principal Problems 2.3- Orbital Integrals 2.4- Examples of Radon Transforms for Homogeneous Spaces in Duality 3.- The Radon Transform on Two-Point Homogeneous Spaces 3.1- Spaces of Constant Curvature: Inversion and Support Theorems 3.2- Compact Two-Point Homogeneous Spaces: Applications 3.3- Noncompact Two-Point Homogeneous Spaces 3.4- Support Theorems Relative to Horocycles 4.- The X-Ray Transform on a Symmetric Space 4.1- Compact Symmetric Spaces: Injectivity and Local Inversion: Support Theorem 4.2- Noncompact Symmetric Spaces: Global Inversion and General Support Theorem 4.3- Maximal Tori and Minimal Spheres in Compact Symmetric Spaces 5.- Orbital Integrals 5.1- Isotropic Spaces 5.2- Orbital Integrals 5.3- Generalized Riesz Potentials 5.4- Determination of a Function from its Integral over Lorentzian Spheres 5.5- Orbital Integrands and Huygens' Principle 6.- The Mean-Value Operator 6.1- An Injectivity Result 6.2- Asgeirsson's Mean-Value Theorem Generalized 6.3- John's Indentities 7.- Fourier Transforms and Distribution: A Rapid Course 7.1-The Topology of Spaces D(Rn), E(Rn) and S(Rn) 7.2- Distribution 7.3- Convolutions 7.4- The Fourier Transform 7.5- Differential Operators with Constant Coefficients 7.6- Riesz Potentials 8.- Lie Transformation Groups and Differential Operators 8.1- Manifolds and Lie Groups 8.2- Lie Transformation Groups and Radon Transforms 9.- Bibliography 10.- Notational Conventions 11.- Index.
371 citations
TL;DR: In this article, the authors apply localization techniques to compute the partition function of a two-dimensional R-symmetric theory of vector and chiral multiplets on S2, where the path integral reduces to a sum over topological sectors of a matrix integral over the Cartan subalgebra of the gauge group.
Abstract: We apply localization techniques to compute the partition function of a two-dimensional \({\mathcal{N}=(2,2)}\) R-symmetric theory of vector and chiral multiplets on S2. The path integral reduces to a sum over topological sectors of a matrix integral over the Cartan subalgebra of the gauge group. For gauge theories which would be completely Higgsed in the presence of a Fayet–Iliopoulos term in flat space, the path integral alternatively reduces to the product of a vortex times an antivortex partition functions, weighted by semiclassical factors and summed over isolated points on the Higgs branch. For applications, we evaluate the partition function for some U(N) gauge theories, showing equality of the path integrals for theories conjectured to be dual by Hori and Tong and deriving new expressions for vortex partition functions.
337 citations
Book•
31 Aug 1990TL;DR: In this article, an introductory account of commutative algebra is given, providing a foundation from which the reader can progress to more advanced works in algebraic geometry or algebraic algebra.
Abstract: This is an introductory account of commutative algebra. The author's intention is to provide a foundation from which the reader can progress to more advanced works in commutative algebra or algebraic geometry.
333 citations
TL;DR: A general form of the first law of thermodynamics for stationary black holes is derived and the density of states is expressed as a real-time functional integral and then used to deduce Feynman's imaginary- time functional integral for the canonical partition function.
Abstract: The gravitational field in a spatially finite region is described as a microcanonical system. The density of states $\ensuremath{
u}$ is expressed formally as a functional integral over Lorentzian metrics and is a functional of the geometrical boundary data that are fixed in the corresponding action. These boundary data are the thermodynamical extensive variables, including the energy and angular momentum of the system. When the boundary data are chosen such that the system is described semiclassically by any real stationary axisymmetric black hole, then in this same approximation $\mathrm{ln}\ensuremath{
u}$ is shown to equal \textonequarter{} the area of the black-hole event horizon. The canonical and grand canonical partition functions are obtained by integral transforms of $\ensuremath{
u}$ that lead to "imaginary-time" functional integrals. A general form of the first law of thermodynamics for stationary black holes is derived. For the simpler case of nonrelativistic mechanics, the density of states is expressed as a real-time functional integral and then used to deduce Feynman's imaginary-time functional integral for the canonical partition function.
303 citations
TL;DR: In this article, a transformation formula for the nonhomogeneous transformation-translation plus linear homogeneous transformation was derived for the Wiener integral, which was then applied to the special linear transformation.
Abstract: Introduction. Let C be the space of all real-valued functions x(t) continuous in 0 < t ?1, and vanishing at t = 0. Wiener has defined a measure over the space C and in terms of this measure he has defined an average or integral over C which is intimately related among other things to the theory of the Brownian motion [1, 2](1). The present authors have recently investigated certain aspects of the Wiener integral [3, 4] and have obtained for instance in [4] a result which shows how the integral is transformed under translations. Irn the present paper we determine how the integral transforms under a certain class of linear homogeneous transformations. This result is also combined with the earlier result on translations to yield a transformation formula for the nonhomogeneous transformation-translation plus linear homogeneous transformation. By applying the transformation formula to the special linear transformation
166 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 11 |
| 2020 | 11 |
| 2019 | 20 |
| 2018 | 10 |
| 2017 | 19 |
| 2016 | 17 |