نتایج جستجو برای: harmonic polynomial
تعداد نتایج: 144090 فیلتر نتایج به سال:
In present work we consider C∗-algebras C∗(Af ) associated with simple unimodal nonbijective dynamical system (f,R) with special requirements. In the case when f is polynomial, Af = C〈X,X∗| XX∗ = f(X∗X)〉 and C∗(Af ) is its enveloping C∗-algebra. As typical examples we consider one-parameter family fμ(x) = μx(1 − x) and two-parameter family called Unharmonic Quantum Oscillator fp,q(x) = 1+ px− q...
We give an extension of Pizzetti’s formula associated with the Dunkl operators. It gives explicit for inner product arbitrary function and a homogeneous harmonic polynomial on unit sphere.
Harmonic and analytic functions have natural discrete analogues. Harmonic functions can be defined on every graph, while analytic functions (or, more precisely, holomorphic forms) can be defined on graphs embedded in orientable surfaces. Many important properties of the “true” harmonic and analytic functions can be carried over to the discrete setting. We prove that a nonzero analytic function ...
Motivated by Gauss’s first proof of the Fundamental Theorem of Algebra, we study the topology of harmonic algebraic curves. By the maximum principle, a harmonic curve has no bounded components; its topology is determined by the combinatorial data of a noncrossing matching. Similarly, every complex polynomial gives rise to a related combinatorial object that we call a basketball, consisting of a...
Given information about a harmonic function in two variables, consisting of a nite number of values of its Radon projections, i.e., integrals along some chords of the unit circle, we study the problem of interpolating these data by a harmonic polynomial. With the help of symbolic summation techniques we show that this interpolation problem has a unique solution in the case when the chords form ...
A method for the evaluation of the ε-expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums. Algorithms for the evaluation of nested and harmonic sums are used to reduce the expressions to get analytical or numerical results for the expansion coefficients. Met...
The fundamental theorem of algebra (FTA) tells us that every complex polynomial of degree n has precisely n complex roots. The first published proofs (J. d’Alembert in 1746 and C. F. Gauss 1799) of this conjecture from the seventeenth century had flaws, though Gauss’s proof was generally accepted as correct at the time. Gauss later published three correct proofs of the FTA (two in 1816 and the ...
In the present paper, the Liouville theorem and the finite dimension theorem of polynomial growth harmonic functions are proved on Alexandrov spaces with nonnegative Ricci curvature in the sense of Sturm, Lott-Villani and Kuwae-Shioya.
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