Related papers: A proof of Fatou's interpolation theorem
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
Reconstruction theorem for the Moufang loops is proved.
This is the second combinatorial proof of the compactness theorem for singular from 1977. In fact it gives a somewhat stronger theorem.
In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.
We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
We prove a generalization of Fulton's conjecture which relates intersection theory on an arbitrary flag variety to invariant theory.
According to Lidstone interpolation theory, an entire function of exponential type $<\pi$ is determined by it derivatives of even order at $0$ and $1$. This theory can be generalized to several variables. Here we survey the theory for a…
We present a generalization of Warning's Second Theorem to polynomial systems over a finite local principal ring with suitably restricted input and output variables. This generalizes a recent result with Forrow and Schmitt (and gives a new…
We obtain some results related to Romanoff's theorem.
We present a simple, PDE-based proof of the result [M. Johnson, 2001] that the error estimates of [J. Duchon, 1978] for thin plate spline interpolation can be improved by $h^{1/2}$. We illustrate that ${\mathcal H}$-matrix techniques can…
In this note we provide a new proof of the Tikhonov theorem for the infinite time interval and discuss some of its applications.
We use Priestley duality to give a new proof of the Hofmann-Mislove Theorem.
In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.
The Gasca-Maeztu conjecture for the case $n=4$ was proved for the first time in [J. R. Busch, A note on Lagrange interpolation in $\mathbb{R}^2$, Rev. Un. Mat. Argentina, 36 (1990) 33--38]. Here we bring a short and simple proof of it.
The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
We extend Prekopa's Theorem and the Brunn-Minkowski Theorem from convexity to $F$-subharmonicity. We apply this to the interpolation problem of convex functions and convex sets introducing a new notion of "harmonic interpolation" that we…
We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.
We give a proof of the uniform convergence of Fourier series, using the methods of nonstandard analysis.