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On the approximation of real continuous functions by series of solutions of a single system of partial differential equations

100%

Elsner C.

Colloquium Mathematicum

2006

tom 104

nr 1

57-84

We prove the existence of an effectively computable integer polynomial P(x,t₀,...,t₅) having the following property. Every continuous function $f: ℝ^{s} → ℝ$ can be approximated with arbitrary accuracy by an infinite sum $∑_{r=1}^{∞} H_{r}(x₁,...,x_{s}) ∈ C^{∞}(ℝ^{s})$ of analytic functions $H_{r}$, each solving the same system of universal partial differential equations, namely $P(x_{σ};H_r,∂H_{r}/∂x_{σ},...,∂⁵H_{r}/∂x⁵_{σ}⁵) = 0$ (σ = 1,..., s).

Algebraic independence results for reciprocal sums of Fibonacci numbers

51%

Elsner C., Shimomura S., Shiokawa I.

Acta Arithmetica

2011

tom 148

nr 3

205-223

Algebraic relations for reciprocal sums of Fibonacci numbers

51%

Elsner C., Shimomura S., Shiokawa I.

Acta Arithmetica

2007

tom 130

nr 1

37-60

Ograniczanie wyników

2 Acta Arithmetica

1 Colloquium Mathematicum

3 Elsner C.

2 Shimomura S.

2 Shiokawa I.

1 2011

1 2007

1 2006

Wyniki wyszukiwania

On the approximation of real continuous functions by series of solutions of a single system of partial differential equations

Algebraic independence results for reciprocal sums of Fibonacci numbers

Algebraic relations for reciprocal sums of Fibonacci numbers