arXiv subjects

Hülya Duru

Publications and source records attributed to Hülya Duru.

4 recordsLinked to original sources

arXiv2026

Hölder Selections under Stieltjes Clocks: Uniform Disconnectedness and Jump Dominance

It is known that, for ordinary Hölder multifunctions with 0 < α < 1, Hölder regularity alone does not guarantee the existence of a Hölder selection, and in general even a continuous selection may fail to exist. We ask how this situation changes when the parameter is measured through a Stieltjes clock. For 0 < α < 1, we characterize the clocks for which every compact-valued g-Hölder multifunction admits a g-Hölder selection. The determining condition is uniform disconnectedness of the clock image Im(g). For left-continuous and nondecreasing clocks, this condition is equivalent to uniform jump dominance: every positive clock increment contains a jump carrying a fixed positive fraction of that increment. Under this condition, a selection can be chosen through any prescribed point of the graph, with explicit control of its Hölder regularity. Conversely, when the condition fails, there exists a compact-valued g-Hölder multifunction with no g-Hölder selection. The results show that the selection property is governed not simply by the presence of jumps, but by how their sizes are distributed across scales.

math.GN↗

arXiv2026

Super-g-Hölder Regularity in Stieltjes Dynamics: Atomic Structure, Exact Extremal Values, and Recovery of the Stieltjes Clock

Unlike ordinary time, a Stieltjes clock may advance continuously, remain constant over intervals, or jump. For an ordinary continuous clock, Hölder regularity with exponent $α>1$ forces constancy, whereas jumps of a Stieltjes clock may allow nonconstant behavior. We refer to Hölder regularity of exponent $α>1$ measured relative to g as super-g-Hölder regularity, and show that, in finite dimensions, such functions admit an atomic representation determined entirely by their jumps, with their g-Hölder seminorms given exactly by the corresponding normalized jump sizes. This atomic representation yields a linear isometric description of the associated function space, together with its Banach and separability properties, an exact total-variation formula with an optimal bound, and finite-jump approximation results. We then apply this structure to Stieltjes differential equations. Nonzero state jumps require positive clock jumps, leading to quantitative finite-jump bounds and, for affine dynamics, exact thresholds for the number of jumps and extremal terminal distances under a prescribed total Stieltjes mass. Finally, we study recovery of the Stieltjes clock from observed state jumps. For known single-valued dynamics, clock jumps can be recovered under a natural local identifiability condition, while for nonconvex differential inclusions the super-g-Hölder bound can reduce, and in some cases remove, nonuniqueness.

math.CA↗

arXiv2026

Selections of Set-Valued Maps under Stieltjes Clocks: Regularity, Variation, and Atomic Structure

A Stieltjes clock allows effective time to advance continuously, remain unchanged over intervals, or jump. We study whether a compact-valued set-valued map evolving relative to a Stieltjes clock admits a single-valued selection that passes through a prescribed graph point while retaining the regularity and variation of the multifunction. For g-Hölder exponents $α\geq 1$, we prove that regularity can be preserved without increasing the g-Hölder seminorm, with no monotonicity assumption on g. If g is additionally nondecreasing, one prescribed-point selection preserves both this regularity and the Hausdorff variation on every subinterval. The same selection consequently preserves all finite Riesz p-variations associated with nondecreasing external clocks. For $α>1$, the structure becomes jump-driven. For left-continuous nondecreasing Stieltjes clocks, continuous clock evolution cannot generate variation: all variation is carried by jumps. We obtain exact jump decompositions for both the set-valued map and its selection, together with explicit atomic formulas for Riesz p-variation. Examples show that the principal regularity, variation, and jump bounds are attained. For compact-convex Euclidean-valued maps, we also examine the case $0<α<1$. In this setting, the Hölder exponent can still be preserved, but preservation of the same constant through a prescribed point holds in one dimension and can fail in higher dimensions. Finally, without a quantitative Hölder bound, we characterize exactly when every compact-valued Hausdorff g-continuous map admits a prescribed-point g-continuous selection: precisely when the clock image is zero-dimensional.

math.DS↗

arXiv2019

Pre-Markov Operators

A positive linear operator $T$ between two unital $f$-algebras, with point separating order duals, $A$ and $B$ is called a Markov operator for which $% T\left( e_{1}\right) =e_{2}$ where $e_{1},e_{2}$ are the identities of $A$ and $B$ respectively. Let $A$ and $B$ be semiprime $f$-algebras with point separating order duals such that their second order duals $A^{\sim \sim }$ and $B^{\sim \sim }$ are unital $f$-algebras. In this case, we will call a positive linear operator $T:A\rightarrow B$ \ to be a Pre-Markov operator, if the second adjoint operator of $T$ is a Markov operator. A positive linear operator $T$ between two semiprime $f$-algebras, with point separating order duals, $A$ and $B$ is said to be contractive if $Ta\in B\cap \left[ 0,I_{B}\right] $ whenever $a\in A\cap \left[ 0,I_{A}\right] $, where $I_{A}$ and $I_{B}$ are the identity operators on $A$ and $B$ respectively. In this paper we characterize pre-Markov algebra homomorphisms. In this regard, we show that a pre-Markov operator is an algebra homomorphism if and only if its second adjoint operator is an extreme point in the collection of all Markov operators from $A^{\sim \sim }$ to $B^{\sim \sim }$. Moreover we characterize extreme points of contractive mappings from $A$ to $B$. In addition, we give a condition that makes an order bounded algebra homomorphism is a lattice homomorphism.

math.FA↗