Operator Theory and Harmonic Analysis

This volume is part of the collaboration agreement between Springer and the ISAAC society.

This is the second in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University, Rostov-on-Don, Russia. This volume focuses on mathematical methods and applications of probability and statistics in the context of general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multi-parameter objects required when considering operators and objects with variable parameters.

Introduces new results in methods, problems and applications of operator theory and harmonic analysis by leading researchers Presents the fundamentals of theory followed by recent developments in PDE's, mathematical modelling, bioinformatics, and a discussion of real-world problems Focuses on the very new trends in operator theory and function spaces theory, such as variable exponent spaces and objects of variable nature

Inhalt
On Solvability of One Nonlinear Integral Equation Arising in Modelling of Geographical Spread of Epidemics.- Hierarchical Schrödinger type operators: the case of locally bounded potentials.- Symmetric Integrals and the Pathwise-Determined Maximum Principle.- Lanchester Model with the Random Coefficients.- Local time and local reflection of the Wiener process.- Out-of-sample utility bounds for empirically optimal portfolios in a single-period investment problem.- A Guaranteed Deterministic Approach to Superhedging: Optimal Mixed Strategies of the Market and their Supports.- CVaR hedging in defaultable Jump-Diffusion markets.- A model for the outbreak of COVID-19: Vaccine effectiveness in a case study of Italy.- Combinatorial IdentitiesWith Binomial Coefficients.- Double-Barrier Option Pricing under the Hyper-Exponential Jump-Diffusion Model.- A probabilistic interpretation of conservation and balance laws.- Random Tempered Distributions on Locally Compact Separable Abelian Groups.- A conditional functional limit theorem for a decomposable branching process.- Influence of the configuration of particle generation sources on the behavior of branching walks: a case study.- Some Properties of Regularly Varying Functions and Series in the Orthant.- On solutions of stochastic equations with current and osmotic velocities.- A Simple Wiener-Hopf Factorization Approach for Pricing Double Barrier Options.- Rate of convergence to the Poisson law of the numbers of cycles in the generalized random graphs.- Single Jump Filtrations: Preservation of the Local Martingale Property with Respect to the Filtration Generated by the Local Martingale.- New procedure for applying the Cramér-von Mises test for parametric families of distributions.- Stochastic methods in investigation of modern networks.- Random harmonic processes with new properties.<p