S. Catoiu

activity

20152026

most citedTwo Pointwise Characterizations of the Peano Derivative

1 citations · 1 across the 7 of their papers we have counts for

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Showing 2022Show all

5 papers · 1 filter

math.CA2022

Gaussian Riemann Derivatives

J. M. Ash, S. Catoiu, H. Fejzic

J. Marcinkiewicz and A. Zygmund proved in 1936 that, for all functions $f$ and points $x$ , the existence of the $n$ th Peano derivative $f_{(n)} (x)$ is equivalent to the existence o…

math.CA2022

A Generalization of the GGR Conjecture

S. Catoiu, H. Fejzic

For each positive integer $n$ , function $f$ , and point $c$ , the GGR Theorem states that $f$ is $n$ times Peano differentiable at $c$ if and only if $f$ is $n - 1$ times Peano differe…

math.CA2022

Counterexamples to the Gaussian vs. MZ derivatives Conjecture

J. Marshall Ash, Stefan Catoiu

J. Marcinkiewicz and A. Zygmund proved in 1936 that the special $n$ -th generalized Riemann derivative $_{2} D_{n} f (x)$ with nodes $0, 1, 2, 2^{2}, \dots, 2^{n - 1}$ , is equivalent to the $n$ …

math.CA2022★ 1 cited

Two Pointwise Characterizations of the Peano Derivative

J. Marshall Ash, Stefan Catoiu, Hajrudin Fejzić

We provide the first two examples of sets of generalized Riemann derivatives of orders up to $n$ , $n \geq 2$ , whose simultaneous existence for all functions~ $f$ at~ $x$ is equivalent…

math.RT2022

Shapovalov Elements For $U_q(\mathfrak{sl}(N+1))

Stefan Catoiu, Ian M. Musson

For a simple Lie algebra, Shapovalov elements give rise to highest weight vectors in Verma modules. The usual construction of these elements uses induction on the length of a certa…