منابع مشابه
Numerical Schemes for Multi Phase Quadrature Domains
In this work, numerical schemes to approximate the solution of one and multi phase quadrature domains are presented. We shall construct a monotone, stable and consistent finite difference method for both one and two phase cases, which converges to the viscosity solution of the partial differential equation arising from the corresponding quadrature domain theory. Moreover, we will discuss the nu...
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We present a novel design for quadrature phase detection utilizing two-mode optical waveguides for optical interferometric systems. A pair of interferometric signals having quadrature optical phase information can be obtained from the near-field and far-field patterns of a two-mode waveguide output. The operational principle is based on a pi/2 differential phase shift between two modal beams oc...
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Formulas like (0.1) and (0.2) are called quadrature identities, and the corresponding domains of integration are called (classical) quadrature domains. Various classes of quadrature domains have been known for quite some time, see e.g. Neumann’s papers [39, 40] from the beginning of the last century, but the systematic study began only with the work of Davis [13], and Aharonov and Shapiro [2]. ...
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It is well known that, in the plane, the boundary of any quadrature domain (in the classical sense) coincides with the zero set of a polynomial. We show, by explicitly constructing some four-dimensional examples, that this is not always the case. This confirms, in dimension 4, a conjecture of the second author. Our method is based on the Schwarz potential and involves elliptic integrals of the ...
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This is a selection of facts, old and new, about quadrature domains. The text, written in the form of a survey, is addressed to non-experts and covers a variety of phenomena related to quadrature domains. Such as: the difference between quadrature domains for subharmonic, harmonic and respectively complex analytic functions, geometric properties of the boundary, instability in the reverse Hele-...
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ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2012
ISSN: 0021-7670,1565-8538
DOI: 10.1007/s11854-012-0009-3