Parabolic convolution equations in a bounded region

1970 ◽  
pp. 131-162 ◽  
Author(s):  
M. I. Višik ◽  
G. I. Èskin
Keyword(s):  
Bounded Region ◽  
Convolution Equations

scholarly journals Fields Connected with Particles in Terms of Complex-Riemannian Geometry

1990 ◽  
Vol 45 (2) ◽  
pp. 81-94
Author(s):  
Julian Ławrynowicz ◽  
Katarzyna Kędzia ◽  
Leszek Wojtczak
Keyword(s):  
Field Potential ◽  
Riemannian Metrics ◽  
Interaction Matrix ◽  
Explicit Calculation ◽  
Maxwell System ◽  
Curved Space ◽  
Starting Point ◽  
Autocorrelation Time ◽  
The Fourier Transform ◽  
Convolution Equations

AbstractA complex analytical method of solving the generalised Dirac-Maxwell system has recently been proposed by two of us for a certain class of complex Riemannian metrics. The Dirac equation without the field potential in such a metric appeared to be equivalent to the Dirac-Maxwell system including the field potentials produced by the currents of a particle in question. The method proposed is connected with applying the Fourier transform with respect to the electric charge treated as a variable, with the consideration of the mass as an eigenvalue, and with solving suitable convolution equations. In the present research an explicit calculation based on linearization of the spinor connections is given. The conditions for the motion are interpreted as a starting point to seek selection rules for curved space-times corresponding to actually existing particles. Then the same method is applied to solids. Namely, by a suitable transformation of the configuration space in terms of elements of the interaction matrix corresponding to the Coulomb, exchange, and dipole integrals, the interaction term in the hamiltonian becomes zero, thus leading to experimentally verificable formulae for the autocorrelation time

scholarly journals Almost vanishing polynomials and an application to the Hough transform

2014 ◽  
Vol 13 (08) ◽  
pp. 1450057 ◽  
Author(s):  
Maria-Laura Torrente ◽  
Mauro C. Beltrametti
Keyword(s):  
Hough Transform ◽  
Affine Space ◽  
Bounded Region ◽  
Pattern Recognition Technique ◽  
Local Study ◽  
Affine Hypersurface ◽  
Automated Recognition ◽  
Real Affine ◽  
Necessary And Sufficient ◽  
Recognition Technique

We consider the problem of deciding whether or not an affine hypersurface of equation f = 0, where f = f(x1, …, xn) is a polynomial in ℝ[x1, …, xn], crosses a bounded region 𝒯 of the real affine space 𝔸n. We perform a local study of the problem, and provide both necessary and sufficient numerical conditions to answer the question. Our conditions are based on the evaluation of f at a point p ∈ 𝒯, and derive from the analysis of the differential geometric properties of the hypersurface z = f(x1, …, xn) at p. We discuss an application of our results in the context of the Hough transform, a pattern recognition technique for the automated recognition of curves in images.

Transport and propagation of a perturbation of a flow of a compressible fluid in a bounded region

1987 ◽  
Vol 100 (1) ◽  
pp. 53-81 ◽  
Author(s):  
Giuseppe Geymonat ◽  
P�n�lope Leyland
Keyword(s):  
Compressible Fluid ◽  
Bounded Region

Bergman Spaces on Disconnected Domains

1996 ◽  
Vol 48 (2) ◽  
pp. 225-243
Author(s):  
Alexandru Aleman ◽  
Stefan Richter ◽  
William T. Ross
Keyword(s):  
Measure Zero ◽  
Bergman Spaces ◽  
Dirichlet Space ◽  
Invariant Subspaces ◽  
Compact Set ◽  
Bounded Region ◽  
Area Measure ◽  
Weak Star ◽  
Harmonic Dirichlet Space ◽  
Disconnected Domains

AbstractFor a bounded region G ⊂ ℂ and a compact set K ⊂ G, with area measure zero, we will characterize the invariant subspaces ℳ (under ƒ → zƒ) of the Bergman space (G \ K), 1 ≤ p < ∞, which contain (G) and with dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K. When G \ K is connected, we will see that dim(ℳ/(z - λ)ℳ) = 1 for all λ ∈ G \ K and thus in this case we will have a complete description of the invariant subspaces lying between (G) and (G \ K). When p = ∞, we will remark on the structure of the weak-star closed z-invariant subspaces between H∞(G) and H∞(G \ K). When G \ K is not connected, we will show that in general the invariant subspaces between (G) and (G \ K) are fantastically complicated. As an application of these results, we will remark on the complexity of the invariant subspaces (under ƒ → ζƒ) of certain Besov spaces on K. In particular, we shall see that in the harmonic Dirichlet space , there are invariant subspaces ℱ such that the dimension of ζℱ in ℱ is infinite.

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