Operator Theory and Harmonic Analysis

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

This is the first 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 in Rostov-on-Don, Russia. This volume is focused on 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 topicis related to the study of complex multiparameter 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
Summability to the hilbert transform.- Is every nontrivial hausdorff operator on lebesgue space a non-riesz operator?.- Lebesgue means of trigonometric integrals and their rate of convergence.- Spanne type characterization of parabolic fractional maximal function and its commutators in parabolic generalized Orlicz-Morrey spaces.- A Dirichlet Problem for Non-Elliptic equations and Chebyshev polynomials.- Banach Spaces of Functions Delta-Subharmonic in the Half-Plane.- Spanne-Guliyev type characterization for fractional integral operator and its commutators in generalized Orlicz-Morrey spaces on spaces of homogeneous type.- Inversion of the Weighed Spherical Mean.- Justification of the averaging method for a system with multipoint boundary value conditions.- On Multidimensional Integral Operators with Homogeneous Kernels in Classes with Asymptotics.- On a Riemann boundary value problem with infinite index in the half-plane.- On reflexivity and other geometric properties of Morrey spaces.- Generalized Cauchy-Riemann Equations with Power-law Singularities in Coefficients of Lower Order.- Martingale hardy-amalgam spaces: atomic decompositions and duality.- On initial extensions of mappings.- Some algebraic aspects of Boolean valued analysis.- Robust Estimation of European and Asian Options.- Weighted estimates containing quasilinear operators.- Banach Spaces of Functions Delta-Subharmonic in the Unit Disc.- Some properties of the kernel of a transmutation operator.- Unilateral ball potentials in grand Lebesgue spaces.- A refinement of the Adams theorem on the Riesz potential.- Weighted Hadamard-Bergman convolution operators.- Non-tangential summability of fourier series.- Homogenization, drift, stabilization and destabilization for the Patlak-Keller-Segel systems driven by the indirect taxis and the short-wavelength external signals.- Applying Wavelet Transformations as a Solution for Convolution Type Equations.- Some questions related with extended eigenvalues and extended eigenoperators.- Norms of linear functionals, summability of trigonometric.- Boundary value problems for 3D-Dirac operators and MIT bag model.- A Neumann series of Bessel functions representation for solutions of the radial Dirac system.- On subadditivity for subspace-valued maps.- Repeated Distances and Dot Products in Finite Fields.- On Some Implementations of Fourier Interpolation.- Eigenvalues of tridiagonal Hermitian Toeplitz matrices with perturbations in the off-diagonal corners.- Boundary behaviour of partial derivatives of solutions of certain laplacian-gradient Inequalities and spatial qc maps. <p