Associate Professor Dr Anvarjon Ahmedov's research is grounded in theories and methods found in the ﬁeld of mathematical analysis with application to spectral theory of elliptic diﬀerential operators (particularly Laplace-Beltrami operator) and wavelet expansions, p-adic Fourier series. His research primarily falls into the following themes:
- Localization and summability of eigenfunction expansions of the Laplace-Beltrami operator on unit sphere.
- The spectral decompositions of the elliptic pseudo-diﬀerential operators.
- The convergence of eigenfunction expansions of elliptic operators in closed domain.
- The approximation of integral and solutions of integral equations by wavelets.
- The localizations of spectral decompositions of distributions.
- The almost everywhere convergence of p-adic Fourier series
- Mathematical Modelling of the Heat and Mass transfer processes