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Representation of Functions as Weierstrass- Transforms
Canadian Mathematical Bulletin, 1967 The 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.
H.P. Heinig
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Representation of Weierstrass integral via Poisson integrals
Journal of Mathematical Sciences, 2021In our research, we have presented a second-order linear partial differential equation in polar coordinates. Considering this differential equation on the unit disk, we have obtained a one-dimensional heat equation. It is well-known that the heat equation can be solved taking into account the boundary condition for the general solution on the unit ...
Shutovskyi, Arsen M. +1 more
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Weierstrass Type Representation of Willmore Surfaces in S n
Acta Mathematica Sinica, English Series, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xia, Qiaoling, Shen, Yibing
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Journal of Geometry and Physics, 2017 In this paper we discuss a Weierstrass type representation for minimal surfaces in the3-dimensional Heisenberg group and in the 4-dimensional Damek–Ricci spaces, endowed with left invariant Riemannian or Lorentzian metrics.
Francesco Mercuri, Irène I Onnis
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Weierstrass Representation of Lightlike Surfaces in Lorentz-Minkowski 4-Space
International Electronic Journal of Geometry, 2023We present a Weierstrass-type representation formula which locally represents every regular two-dimensional lightlike surface in Lorentz-Minkowski 4-Space $\mathbb{M}^4$ by three dual functions $(\rho,f,g)$ and generalizes the representation for regular lightlike surfaces in $\mathbb{M}^3$. We give necessary and sufficient conditions on the functions $\
Davor Devald, Z. Milin Sipus
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Weierstrass type representations
2001The theory for finite type solutions developped in Chapter 8 can be generalized in order to represent all harmonic maps from a simply connected surface to symmetric spaces like the sphere S2. This has been developped by J. Dorfmeister, F. Pedit and H.Y. Wu and leads to a Weierstrass type representation [30].
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A Weierstrass representation theorem for Lorentz surfaces
Complex Variables, Theory and Application: An International Journal, 2005We consider functions with values in the algebra of Lorentz numbers which are differentiable with respect to the algebraic structure of as an analogue of holomorphic functions. Then we apply these functions to prove a Weierstrass representation theorem for Lorentz surfaces immersed in the space .
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The global Weierstrass representation and its spectrum
Russian Mathematical Surveys, 1997In this short note the author gives an outline of his results on the global Weierstraß representation of closed oriented surfaces and its spectrum. For details the reader is refered to \textit{I. A. Taimanov} [Am. Math. Soc. Transl. 179(33), 133-151 (1997; Zbl 0896.53006); Ann. Global Anal. Geom. 15, No. 5, 419-435 (1997; Zbl 0896.53007)].
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Weierstrass Representation of Some Simply-Periodic Minimal Surfaces
Annals of Global Analysis and Geometry, 2001In a previous paper [Ann. Inst. Fourier 46, 1385--1442 (1996; Zbl 0860.53004)], the author constructed simply-periodic minimal surfaces by desingularization of a set of vertical planes using the techniques developed by \textit{N. Kapouleas} [Ann. Math. (2) 131, 239--330 (1990; Zbl 0699.53007)].
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A Weierstrass type representation for translating solitons and singular minimal surfaces
Journal of Mathematical Analysis and Applications, 2022Antonio Martinez, A Martinez
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