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Weierstrass Functions Separate All Traces
Mathematical Notes, 2021In this note, the authors generalize a result of [\textit{H.~Gimperlein} and \textit{M.~Goffeng}, Forum Math. Sigma 5, Paper No.~e3, 57~p. (2017; Zbl 1471.58007)] to the case of all traces on the weak \(L_1\)-ideal \(\mathscr{L}_{1,\infty}\). As a corollary, they show that the class of operators related to the quantum differentials of Weierstrass ...
Goffeng, M., Usachev, A. S.
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Applications of the Weierstrass Functions
, 1989Consider the transformation $$z = p(w),$$ (7.1.1) mapping a period parallelogram of p in the w-plane onto the z-plane. We shall suppose ω1 to be real and ω3 to be imaginary, so that the points e α=p(ωα) all lie on the real axis in the z-plane (in the order e 3, e 2, e 1 from the left).
D. F. Lawden
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Fractional integrals of the Weierstrass functions: The exact box dimension
Analysis in Theory and Applications, 2004Weiyi Su, Su Weiyi
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Hausdorff dimension of the graphs of the classical Weierstrass functions
Mathematische Zeitschrift, 2017We show that the graph of the classical Weierstrass function $$\sum _{n=0}^\infty \lambda ^n \cos (2\pi b^n x)$$∑n=0∞λncos(2πbnx) has Hausdorff dimension $$2+\log \lambda /\log b$$2+logλ/logb, for every integer $$b\ge 2$$b≥2 and every $$\lambda \in (1/b ...
Weixiao Shen
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A multivariate Weierstrass–Mandelbrot function
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1985Abstract The univariate Weierstrass–Mandelbrot function is generalized to many variables to model higher dimensional stochastic processes such as undersea topography. Because this topography is difficult to measure at small length scales over the many large regions that affect long-ranged acoustic propagation in the ocean, one needs a
Ausloos, M., Berman, D. H.
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Physica Scripta, 2023
In this paper, the auxiliary equation method is used to study the Weierstrass elliptic function solutions and degenerate solutions of the variable coefficient higher order Schrödinger equation, including Jacobian elliptic function solutions ...
Lulu Fan, Taogetusang Bao
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In this paper, the auxiliary equation method is used to study the Weierstrass elliptic function solutions and degenerate solutions of the variable coefficient higher order Schrödinger equation, including Jacobian elliptic function solutions ...
Lulu Fan, Taogetusang Bao
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2015
The aim of this chapter is to present various classical methods of testing the nowhere differentiability of the Weierstrass-type function \(x\longmapsto \sum _{n=0}^{\infty }a^{n}\cos ^{p}(2\pi b^{n}x +\theta _{n})\).
Marek Jarnicki, Peter Pflug
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The aim of this chapter is to present various classical methods of testing the nowhere differentiability of the Weierstrass-type function \(x\longmapsto \sum _{n=0}^{\infty }a^{n}\cos ^{p}(2\pi b^{n}x +\theta _{n})\).
Marek Jarnicki, Peter Pflug
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On Products of Weierstrass Sigma Functions
Journal of Mathematical Sciences, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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