Convolution equations without non-trivial solutions

1971 ◽  
pp. 53-56
Author(s):  
Tord H. Ganelius
Keyword(s):  
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 The Solvability of a Class of Convolution Equations Associated with 2D FRFT

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1928
Author(s):  
Zhen-Wei Li ◽  
Wen-Biao Gao ◽  
Bing-Zhao Li
Keyword(s):  
Fourier Transform ◽  
Convolution Operator ◽  
Fractional Fourier Transform ◽  
Hankel Transform ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Spatial Shift ◽  
Fractional Hankel Transform ◽  
The Relationship ◽  
Convolution Equations

In this paper, the solvability of a class of convolution equations is discussed by using two-dimensional (2D) fractional Fourier transform (FRFT) in polar coordinates. Firstly, we generalize the 2D FRFT to the polar coordinates setting. The relationship between 2D FRFT and fractional Hankel transform (FRHT) is derived. Secondly, the spatial shift and multiplication theorems for 2D FRFT are proposed by using this relationship. Thirdly, in order to analyze the solvability of the convolution equations, a novel convolution operator for 2D FRFT is proposed, and the corresponding convolution theorem is investigated. Finally, based on the proposed theorems, the solvability of the convolution equations is studied.

scholarly journals Convolution equations in the space of Laplace distributions

1998 ◽  
Vol 69 (3) ◽  
pp. 271-281
Author(s):  
Maria Pliś
Keyword(s):  
Convolution Equations
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