From Classical Analysis to Analysis on Fractals

Part I. Introduction to this volume.- From Strichartz Estimates to Differential Equations on Fractals.- Part II. Functional and harmonic analysis on Euclidean spaces.- A new proof of Strichartz estimates for the Schroedinger equation in 2 + 1 dimensions.- Modulational instability of classical water waves.- Convergence Analysis of the Deep Galerkin Method for Weak Solutions.- The 4-player gambler's ruin problem.- Part III. Analysis on Manifolds.- Product Manifolds with Improved Spectral Cluster and Weyl Remainder Estimates.- A scalar valued Fourier transform for the Heisenberg group.- Asymptotic behavior of the heat semigroup on certain Riemannian manifolds.- Part IV. Intrinsic Analysis on Fractals.- Fourier Series for Fractals in 2 Dimensions.- Blowups and Tops of Overlapping Iterated Function Systems.- Estimates of the local spectral dimension of the Sierpinski gasket.- Heat kernel fluctuations for stochastic processes on fractals and random media.- Index.

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• Probabilidade e Estatística
• Análise funcional e transforma
• Análise complexa, variáveis ??complexas
• Estocástica
• Cálculo integral e equações
• Cálculo diferencial e equações

Robert Strichartz;Strichartz Estimates;Fractals;Harmonic Analysis;Self-Similar Sets;Dirichlet Forms;Riemannian and Sub-Riemannian Manifolds