Examining the behavior of parametric convex operators on a certain set of analytical functions. [PDF]
Aldawish I.
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Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation. [PDF]
Forlano J, Tolomeo L.
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An Attention-based Spatio-Temporal Neural Operator for Evolving Physics. [PDF]
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Stability of Rayleigh-Jeans Equilibria in the Kinetic FPU Equation. [PDF]
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On Subsequential Averages of Sequences in Banach Spaces
Real Analysis Exchange, 2023This paper gives a strong contribution to the solution to the conjecture described next. Conjecture 1. Let \(\mathcal{X}\) be a Banach space, and suppose that \(x=\{x_n\}_{n=0}^{\infty}\subseteq\mathcal{X}\). Then the set \[\overline{x}^c=\left\{y\in\mathcal{X}: \exists \text{ a strictly increasing sequence } \{k_n\}\text{ s.t.
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On the Boundedness of a Recurrence Sequence in a Banach Space
Ukrainian Mathematical Journal, 2003The authors consider the recurrence sequence \[ x_n=\sum\limits_{k=1}^\infty A_kx_{n-k}+y_n,\quad n\geq 1, \] \[ x_n=\alpha_n,\quad n\leq 0, \] in a Banach space \(B\), where the sequences \(\{ y_n\}\) and \(\{ \alpha_n\}\) are bounded, \(A_k\) are bounded linear operators, and \(\sum\limits_{k=1}^\infty k^{1+\epsilon}\| A_k\| 0\). It is shown that the
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