Author_Institution :
Inst. of Radio En. & Electron., Russian Acad. of Sci., Moscow, Russia
Abstract :
Foundations of measure theory, the Hausdorff-Besicovitch measure, fractal nowhere differentiable Boltzano, Weierstrass, Cantor, Riemann, Darboux, Van-der-Waerden, Koch, Sierpinski, Besicovitch, and Weierstrass-Mandelbrot functions, and also some atomic functions possessing fractal properties are considered. For the first time, the atomic-fractal functions are constructed. The theory proposed and justified is illustrated on problems of synthesis of radiating structures by means of modeling the corresponding physical processes.
Keywords :
Fourier transforms; antenna arrays; antenna radiation patterns; antenna theory; array signal processing; fractals; Besicovitch functions; Cantor functions; Darboux functions; Fourier transform; Hausdorff-Besicovitch measure; Koch functions; Riemann functions; Sierpinski functions; Van-der-Waerden functions; Weierstrass functions; Weierstrass-Mandelbrot functions; antenna theory; atomic functions; atomic-fractal functions; differentiable Boltzano; fractal antenna arrays; fractal nowhere differentiable functions; fractal properties; measure theory; radiating structure synthesis; Antenna arrays; Antenna measurements; Antenna theory; Atomic measurements; Density measurement; Fractal antennas; Gaskets; Geometry; Mathematics; Signal synthesis;
