First works related to the topics covered in this book belong to J. Delsarte and B. M. Le vitan and appeared since 1938. In these works, the families of operators that generalize usual translation operators were investigated and the corresponding harmonic analysis was constructed. Later, starting from 1950, it was noticed that, in such constructions, an important role is played by the fact that the kernels of the corresponding convolutions of functions are nonnegative and by the properties of the normed algebras generated by these convolutions. That was the way the notion of hypercomplex...

When solving the control and design problems in aerospace and naval engi neering, energetics, economics, biology, etc., we need to know the state of investigated dynamic processes. The presence of inherent uncertainties in the description of these processes and of noises in measurement devices leads to the necessity to construct the estimators for corresponding dynamic systems. The estimators recover the required information about system state from mea surement data. An attempt to solve the estimation problems in an optimal way results in the formulation of different variational problems. The...

This book deals with linear functional differential equations and operator theory methods for their investigation. The main topics are: the equivalence of the input-output stability of the equation "L"x = &mathsf; and the invertibility of the operator "L" in the class of casual operators; the equivalence of input-output and exponential stability; the equivalence of the dichotomy of solutions for the homogeneous equation "L"x = 0 and the invertibility of the operator "L"; the properties of Green's function; the independence of the stability of an equation from the norm on the space of...

The problems of modern society are complex, interdisciplinary and nonlin- ear. onlinear problems are therefore abundant in several diverse disciplines. Since explicit analytic solutions of nonlinear problems in terms of familiar, well- trained functions of analysis are rarely possible, one needs to exploit various approximate methods. There do exist a number of powerful procedures for ob- taining approximate solutions of nonlinear problems such as, Newton-Raphson method, Galerkins method, expansion methods, dynamic programming, itera- tive techniques, truncation methods, method of upper and...

Advances in science and technology necessitate the use of increasingly-complicated dynamic control processes. Undoubtedly, sophisticated mathematical models are also concurrently elaborated for these processes. In particular, linear dynamic control systems iJ = Ay + Bu, y E M C ]Rn, U E ]RT, (1) where A and B are constants, are often abandoned in favor of nonlinear dynamic control systems (2) which, in addition, contain a large number of equations. The solution of problems for multidimensional nonlinear control systems en counters serious difficulties, which are both mathematical and...

" . . . if a physical system is capable of supporting solitary wave motions then such motions will invariably arise from quite general excitations. " - T. Maxworthy (1980), pg. 52. The discover of nonlocal solitary waves is unknown and anonymous, but he or she lived in the dry north of Australia many millenia before the birth of writing. There, on the shores of the Gulf of Carpentaria, vast cylinders of cloud roll from northeast to southwest most mornings. Perhaps 300 meters in diameter, perhaps 500 meters above the ocean, these cylinders of cloud stretch from horizon to horizon. As the cloud...

This book provides an upto date information on metric, connection and curva ture symmetries used in geometry and physics. More specifically, we present the characterizations and classifications of Riemannian and Lorentzian manifolds (in particular, the spacetimes of general relativity) admitting metric (i.e., Killing, ho mothetic and conformal), connection (i.e., affine conformal and projective) and curvature symmetries. Our approach, in this book, has the following outstanding features: (a) It is the first-ever attempt of a comprehensive collection of the works of a very large number of...

This book is devoted to an investigation of the basic problems of the the ory of random fields which are characterized by certain singular properties (e. g., unboundedness, or vanishing) of their spectral densities. These ran dom fields are called, the random fields with singular spectrum, long-memory fields, random fields with long-range dependence, fields with slowly decaying correlations or strongly dependent random fields by various authors. This phenomenon has been observed empirically by many scientists long before suitable mathematical models were known. The methods and results differ...

The numerous publications on spline theory during recent decades show the importance of its development on modern applied mathematics. The purpose of this text is to give an approach to the theory of spline functions, from the introduction of the phrase spline by I.J. Schoenbergin 1946 to the newest theories of spline-wavelets or spline-fractals, emphasizing the significance of the relationship between the general theory and its applications. In addition, this volume provides material on spline function theory, as well as an examination of basic methods in spline functions. The authors have...

1. Interpolation problems play an important role both in theoretical and applied investigations. This explains the great number of works dedicated to classical and new interpolation problems ( 1)- 5], 8), 13)- 16], 26)- 30], 57]). In this book we use a method of operator identities for investigating interpo lation problems. Following the method of operator identities we formulate a general interpolation problem containing the classical interpolation problems (Nevanlinna Pick, Caratheodory, Schur, Humburger, Krein) as particular cases. We write down the abstract form of the Potapov...