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Functional Equations and Weierstrass Transforms
Results in Mathematics, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Weierstrass elliptic functions
2020This chapter depends on Chapter 14 but not on Chapter 15. Here we look for a more direct approach to elliptic functions with given periods.
Richard Beals, Roderick S. C. Wong
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Pfaffian definitions of Weierstrass elliptic functions
, 2017We give explicit definitions of the Weierstrass elliptic functions $$\wp $$ ℘ and $$\zeta $$ ζ in terms of pfaffian functions, with complexity independent of the lattice involved.
G. Jones, Harry Schmidt
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Representation of Functions as Weierstrass- Transforms
Canadian Mathematical Bulletin, 1967The Weierstrass - respectively Weierstrass - Stieltjes transform of a function F(t) or μ(t) is defined by1.1and1.2for all x for which these integrals converge. In what follows we shall always assume that F(t) is Lebesgue integrable in every finite interval and that μ(t) is a function of bounded variation.
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The Weierstrass Elliptic Function
2020The elliptic functions are meromorphic complex functions, which are periodic in two distinct directions in the complex plane. As such, they are naturally well-defined on the torus. For this reason, they find numerous applications in physics. Although their definition is quite simple, it leads to a particularly rich and beautiful set of properties.
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1966
The basic problem of the Calculus of Variations is that of finding a point in function space at which a given integral attains a maximum or a minimum value. The type of problem that can be solved by means of this calculus is referred to as a variational problem, and the extreme value of the integral is called an extremum. [...]
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The basic problem of the Calculus of Variations is that of finding a point in function space at which a given integral attains a maximum or a minimum value. The type of problem that can be solved by means of this calculus is referred to as a variational problem, and the extreme value of the integral is called an extremum. [...]
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Functional Equations and Weierstrass Transforms II
Results in Mathematics, 1997Results of Part I [ibid. 26, 199-204 (1994; Zbl 0876.39005)] are extended to higher dimensions and certain functional equations of `translation' type are studied.
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FRACTAL GEOMETRY OF WEIERSTRASS-TYPE FUNCTIONS
Fractals, 2009The aim of this paper is twofold. First, with reference to Refs. 1 and 2 we show maximal and minimal box and Hausdorff dimensions over all continuous real functions compactly supported on ℝn, with integrability 0 < p ≤ ∞ and exact smoothness s > 0. We estimate also the box dimensions of trigonometrical Weierstrass-type functions.
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Weierstrass’s Elliptic Function
1989Given the complex parameter τ (with positive imaginary part), the quarter-periods K and iK′ of the Jacobian elliptic functions are determined by the equations (2.2.7) and (2.2.8); according to equation (2.2.3), r is precisely the ratio iK′/K of these quarter-periods.
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