A differential condition for an analytic function of two variables to have one-dimensional stabilizer in the gauge pseudogroup is obtained. A multiplicative representation (by homogeneous functions) of such functions is given. The stabilizer theorem is improved, and two important examples are constructed. Questions are posed.

According to the Wik theorem, there exist massive Helson sets on the circle. In particular, they can be of Hausdorff dimension one. We extend Wik’s result to the multidimensional case.

Based on fixed point theory for condensing operators, an initial value problem for semilinear differential inclusions of fractional order $$q\in(1,2)$$ in Banach spaces is studied. It is assumed that the linear part of the inclusion generates a family of cosine operator functions and the nonlinear part is a multivalued map with nonconvex values. Local and global existence theorems for mild solutions of the initial value problem are proved.

Let $$X$$ be a compact complex space in Fujiki’s class $$\mathcal{C}$$ . In this paper, we show that $$X$$ admits a compact Kähler model $${\tilde X}$$ , that is, there exists a projective bimeromorphic map $$\sigma\colon\tilde{X}\to X$$ from a compact Kähler manifold $$\tilde{X}$$ such that the automorphism group $$\operatorname{Aut}(X)$$ lifts holomorphically and uniquely to a subgroup of $$\operatorname{Aut}({\tilde X})$$ . As a consequence, we also give a few applications to the Jordan property, the finiteness of torsion groups, and arbitrary large finite abelian subgroups for compact complex spaces in Fujiki’s class $${\mathcal C}$$ .

The stationary Kolmogorov equation with partially degenerate diffusion matrix and discontinuous drift coefficient is studied. Sufficient conditions for the existence of a probability solution are obtained. Examples demonstrating the sharpness of these conditions are given.

The paper presents the properties of generalized multiple multiplicative Fourier transforms. Also, upper and lower bounds are given for the integral modulus of continuity in terms of the mentioned Fourier transforms, and the bound in $$L^2$$ is unimprovable. As a corollary, an analog of Titchmarsh’s equivalence theorem for the multiplicative Fourier transform is obtained.

For one generalization of the Riemann differential equation, we obtain sufficient conditions for the approximability by twice continuously differentiable rational interpolation spline functions. To solve the corresponding boundary value problem numerically, a tridiagonal system of linear algebraic equations is constructed and conditions on the coefficients of the differential equation are found guaranteeing the uniqueness of the solution of such Estimates of the deviation of the discrete solution of the boundary value problem from the exact solution on a grid are presented.