From Classical Analysis to Analysis on Fractals

Patricia Alonso Ruiz is an Assistant Professor at Texas A&M University in College Station, US. She did her PhD at the University of Siegen, Germany (2013), after getting her licentiate degree from the Universidad Complutense de Madrid, Spain. Her research mainly deals with analysis and probability on fractals, with a focus on function spaces, functional inequalities, semigroups, and Dirichlet forms.Michael Hinz obtained his doctoral degree from Friedrich Schiller University Jena, Germany, and currently works as Wissenschaftliche Mitarbeiter at Bielefeld University, Germany. His research areas are analysis and probability theory, and he is particularly interested in fractal structures and spaces.Kasso A. Okoudjou is a Professor of Mathematics at Tufts University, USA. He received his Ph.D. in Mathematics from the Georgia Institute of Technology and was an H. C. Wang Assistant Professor at Cornell University. He held positions at the University of Maryland–College Park, Technical University of Berlin, MSRI, and MIT. His research interests include applied and pure harmonic analysis especially time-frequency and time scale analysis, frame theory, and analysis and differential equations on fractals.Luke G. Rogers has a Ph.D. from Yale University and is a Professor of Mathematics at the University of Connecticut. His research is primarily in harmonic and functional analysis on metric measure spaces, especially those with fractal structure.Alexander Teplyaev is a Professor of Mathematics at the University of Connecticut, USA. He studied probability and mathematical physics in St.Petersburg and at Caltech, has a Ph.D. degree in mathematics from Cornell University, and was a postdoctoral researcher at McMaster University and the University of California with a National Science Foundation fellowship. He also was supported by the Alexander von Humboldt Foundation in Germany and by the Fulbright Program in France. Teplyaev studies irregular structures, such as random or aperiodic non-smooth media, graphs, groups, and fractals. His research deals with spectral, geometric, functional, and probabilistic analysis on singular spaces using symmetric Markov processes and Dirichlet form techniques.

• Preface.- The Einstein Relation on Metric Measure Spaces.- Numerical investigation of Holder exponent for harmonic functions on Sierpinski Carpets.- Fractal Complex Dimensions and Cohomology of the Weierstrass Curve.- Surjectivity of spectral multipliers on p.c.f. fractals.- Scaling limit of the sandpile identity element on the Sierpinski gasket.- 𝑝-Energy forms on fractals: recent progress.- Generalised Kre˘ın–Feller operators and gap diffusions via transformations of measure spaces.- Strichartz inequalities: some recent developments.- Self-similar energies on Fractals obtained by anti-attracting maps.- Fractal curvatures and short-time asymptotics of heat content.