Lectures on Fourier Integrals

  title={Lectures on Fourier Integrals},
  author={Ruel Vance Churchill and Salomon Bochner and Morris Tenenbaum and Harry S. Pollard},
How to Explicitly Calculate Feynman and Wheeler Propagators in the ADS/CFT Correspondence
We discuss, giving all necessary details, the boundary-bulk propagators. We do it for a scalar field, with and without mass, for both the Feynman and the Wheeler cases. Contrary to standardExpand
A New Composition Method of Admissible Support Vector Kernel Based on Reproducing Kernel
A new algorithm that can obtain the unified explicit form of R.K in general reproducing kernel Hilbert space is presented and it avoids constructing and solving the complex differential equations manually and benefits an automatic, flexible and rigorous computation for more general RKHS. Expand
Models for the difference of continuous covariance functions
  • D. Posa
  • Stochastic Environmental Research and Risk Assessment
  • 2021
A linear combination, with negative weights, of two continuous covariance functions has been analyzed by a few authors just for special cases and only in the real domain. However, a covariance is aExpand
Bayesian Inference for Big Spatial Data Using Non-stationary Spectral Simulation
This article uses Mejia and Rodriguez-Iturbe (1974)'s spectral simulation approach to simulate a spatial process with a covariogram at locations that have an expanded dimension, and introduces Bayesian hierarchical modelling to dimension expansion. Expand
Strict positive definiteness in geostatistics
  • S. De Iaco, D. Posa
  • Mathematics
  • Stochastic Environmental Research and Risk Assessment
  • 2017
Geostatistical modeling is often based on the use of covariance functions, i.e., positive definite functions. However, when interpolation problems have to be solved, it is advisable to consider theExpand
The Error Probability of Random Fourier Features is Dimensionality Independent
Compared to prior work, this work is the first to show that the error probability for random Fourier features is independent of the dimensionality of data points as well as the size of their domain. Expand
Strict Positive Definiteness of a Product of Covariance Functions
Positive definiteness represents an admissibility condition for a function to be a covariance. Nevertheless, the more restricted condition of strict positive definiteness has received attention inExpand
Approximation of high-dimensional kernel matrices by multilevel circulant matrices
This paper introduces an approximation of the kernel matrices by appropriate multilevel circulant matrices so that the fast Fourier transform can be applied to reduce the computational cost. Expand
On a progress in the Kontorovich–Lebedev transform theory and related integral operators
This survey represents mainly recent results of the author, which were obtained during the last decade and concern the theory of the Kontorovich–Lebedev transformation and some related integralExpand
On the absolutely and singularly continuous sub-spaces in scattering theory
A physical criterion is described to distinguish between absolutely continuous and singularly continuous subspaces of a Hamiltonian. Some models are discussed in this connection.