Trigonometric transformation of functions of several real variables in the study and approximation of functions

Source abstract

Aim . Defining the transformation of a set of functions of two real variables based on the concept of a directional derivative, representing methods for applying the transformation to explore functions and their approximation, constructing numerical methods and determining the transformation for functions of more variables. Methodology . Analysis of the theory of sets and their mappings, including mappings of a set of functions, the use of relevant sections of the theory of mathematical analysis, including the transformation of functions and the expansion of non-periodic and periodic functions into series, the theory of constructing numerical methods for approximating functions. Results . The transformation of functions of two real variables is defined, methods of applying the transformation to study functions in the vicinity of a given point and expansion of functions into special functional series are described, centrifugally periodic functions of two variables are defined, numerical methods for approximating functions of two variables are constructed, and transformation of functions of a larger number of variables is defined. Research implications . The presented transformation of functions of several variables is an element of the further development of the theory of functions and functional analysis; the described methods of its use expand the directions for research of this theory, including the area of expansion of functions of several variables into functional series. The theoretical results obtained can be used in applied problems of mathematical modeling, including the use of centrifugally periodic functions for modeling wave processes (in seismology, explosion physics and other fields), in approximating functions using the presented numerical methods, and in the development of new numerical methods.