Alexandre B. Simas

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math.AP2025

Spectral Theory of Krein-Feller Type Operators and Applications in Stochastic Fractional Elliptic and Parabolic Equations

Kelvin J. R. Almeida-Sousa, Alexandre B. Simas

It has been shown that the space $C_{W, V}^{\infty} (T)$ , introduced in Simas and Sousa (Potential Analysis, 2025), is the natural regularity space for solutions of the eige…

math.AP2025

One-sided measure theoretic elliptic operators and applications to SDEs driven by Gaussian white noise with atomic intensity

Alexandre B. Simas, Kelvin J. R. Sousa

We define the operator $D_{V}^{+} D_{W}^{-} := I^_{W, V}$ on the one-dimensional torus $T$ . Here, $W$ and $V$ are functions inducing (possibly atomic) positive Borel measures on $\mat…