Ural Mathematical Journal (UMJ)
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ON -CONVERGENCE ALMOST EVERYWHERE OF MULTIPLE TRIGONOMETRIC FOURIER SERIES
No full textWe consider one type of convergence of multiple trigonometric Fourier series intermediate between the convergence over cubes and the -convergence for . The well-known result on the almost everywhere convergence over cubes of Fourier series of functions from the class has been generalized to the case of the -convergence for some sequences
CONVERGENCE OF SOLUTIONS OF BILATERAL PROBLEMS IN VARIABLE DOMAINS AND RELATED QUESTIONS
Get PDFWe discuss some results on the convergence of minimizers and minimum values of integral and more general functionals on sets of functions defined by bilateral constraints in variable domains. We consider the case of regular constraints, i.e., constraints lying in the corresponding Sobolev space, and the case where the lower constraint is zero and the upper constraint is an arbitrary nonnegative function. The first case concerns a larger class of integrands and requires the positivity almost everywhere of the difference between the upper and lower constraints. In the second case, this requirement is absent. Moreover, in the latter case, the exhaustion condition of an n-dimensional domain by a sequence of n-dimensional domains plays an important role. We give a series of results involving this condition. In particular, using the exhaustion condition, we prove a certain convergence of sets of functions defined by bilateral (generally irregular) constraints in variable domains
A CHARACTERIZATION OF EXTREMAL ELEMENTS IN SOME LINEAR PROBLEMS
Get PDFWe give a characterization of elements of a subspace of a complex Banach space with the property that the norm of a bounded linear functional on the subspace is attained at those elements. In particular, we discuss properties of polynomials that are extremal in sharp pointwise Nikol'skii inequalities for algebraic polynomials in a weighted -space on a finite or infinite interval
AUTOMORPHISMS OF DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {25; 16; 1; 1; 8; 25}
Get PDFMakhnev and Samoilenko have found parameters of strongly regular graphs with no more than 1000 vertices, which may be neighborhoods of vertices in antipodal distance-regular graph of diameter 3 and with . They proposed the program of investigation vertex-symmetric antipodal distance-regular graphs of diameter 3 with , in which neighborhoods of vertices are strongly regular. In this paper we consider neighborhoods of vertices with parameters
CALIBRATION RELATIONS FOR ANALOGUES OF THE BASIS SPLINES WITH UNIFORM NODES
Get PDFThe paper deals with generalized linear and parabolic B-splines with the uniform nodes constructed by means only one function . For such splines in this paper conditions have been found that guarantee satisfaction of two-scale relations
APPROXIMATION BY LOCAL PARABOLIC SPLINES CONSTRUCTED ON THE BASIS OF INTERPOLATION IN THE MEAN
Get PDFThe paper deals with approximative and form-retaining properties of the local parabolic splines of the form where is a normalized parabolic spline with the uniform nodes and functionals are given for an arbitrary function defined on by means of the equalities On the class of functions under , the approximation error value is calculated exactly for the case of approximation by such splines in the uniform metrics
DIVERGENCE OF THE FOURIER SERIES OF CONTINUOUS FUNCTIONS WITH A RESTRICTION ON THE FRACTALITY OF THEIR GRAPHS
Get PDFWe consider certain classes of functions with a restriction on the fractality of their graphs. Modifying Lebesgue’s example, we construct continuous functions from these classes whose Fourier series diverge at one point, i.e. the Fourier series of continuous functions from this classes do not converge everywhere
ON INTERPOLATION BY ALMOST TRIGONOMETRIC SPLINES
Get PDFThe existence and uniqueness of an interpolating periodic spline defined on an equidistant mesh by the linear differential operator with are reproved under the final restriction on the step of the mesh. Under the same restriction, sharp estimates of the error of approximation by such interpolating periodic splines are obtained
NEW METHOD OF REFLECTOR SURFACE SHAPING TO PRODUCE A PRESCRIBED CONTOUR BEAM
Get PDFIn this paper a simple iterative synthesis method is presented for the formation of the shape of the reflector surface with a single feed element to produce the desired contour beam. This is the method of the optimal phase synthesis of the appropriate field in the reflector aperture similar to other works. But unlike them, we solve the problem in a very simple way using the properties of complex-valued functions and Fourier transforms and not applying complicated methods of numerical minimization theory
ON THE OSCILLATION OF A THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH NEUTRAL TYPE
Get PDFIn this article, we investigate that oscillation behavior of the solutions of the third-order nonlinear differential equation with neural type of the formwhere . Some new oscillation results are presented that extend those results given in the literature