Problems · OpenFrontiers

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Erdős #1152 · analysis / polynomials

For n geq 1 fix some sequence of n distinct numbers x 1n , ldots,x nn in [-1,1] . Let epsilon= epsilon(n) to 0 . Does there always exist a continuous function f:[-1,1] to mathbb R such that if p n is a …

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OP-9373AnalysisOpen

Erdős #1151 · analysis / polynomials

Given a 1, ldots,a n in [-1,1] let mathcal L ^nf(x) = sum 1 leq i leq n f(a i) ell i(x) be the unique polynomial of degree n-1 which agrees with f on a i for 1 leq i leq n (that is, the Lagrange inte…

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OP-9372AnalysisOpen

Erdős #1150 · analysis / polynomials

Does there exist a constant c 0 such that, for all large n and all polynomials P of degree n with coefficients pm 1 , max lvert z rvert=1 lvert P(z) rvert (1+c) sqrt n ?

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OP-9363AnalysisOpen

Erdős #1133 · analysis / polynomials

Let C 0 . There exists epsilon 0 such that if n is sufficiently large the following holds. For any x 1, ldots,x n in [-1,1] there exist y 1, ldots,y n in [-1,1] such that, if P is a polynomial of degree $m<(…

Erdős Problems (Thomas Bloom)· Source reports OPEN

OP-9362AnalysisOpen

Erdős #1132 · analysis / polynomials

For x 1, ldots,x n in [-1,1] let l k(x)= frac prod i neq k (x-x i) prod i neq k (x k-x i) , which are such that l k(x k)=1 and l k(x i)=0 for i neq k . Let x 1,x 2, ldots in [-1,1] be an infinite s…

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OP-9361AnalysisOpen

Erdős #1131 · analysis / polynomials

For x 1, ldots,x n in [-1,1] let l k(x)= frac prod i neq k (x-x i) prod i neq k (x k-x i) , which are such that l k(x k)=1 and l k(x i)=0 for i neq k . What is the minimal value of I(x 1, ldots,x…

Erdős Problems (Thomas Bloom)· Source reports OPEN

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Erdős #1152 · analysis / polynomials

Erdős #1151 · analysis / polynomials

Erdős #1150 · analysis / polynomials

Erdős #1133 · analysis / polynomials

Erdős #1132 · analysis / polynomials

Erdős #1131 · analysis / polynomials