Integrální počet II [Book]
Integrals and Banach spaces for finite order distributions
Let denote the real-valued functions continuous on the extended real line and vanishing at . Let denote the functions that are left continuous, have a right limit at each point and vanish at . Define to be the space of tempered distributions that are the th distributional derivative of a unique function in . Similarly with from . A type of integral is defined on distributions in and . The multipliers are iterated integrals of functions of bounded variation. For each , the spaces...
Integralungleichungen aus der Hilbertraum-Theorie.
Integration and decompositions of weak-integrable multifunctions
Conditions guaranteeing Pettis integrability of a Gelfand integrable multifunction and a decomposition theorem for the Henstock-Kurzweil-Gelfand integrable multifunctions are presented.
Integration by Parts
Integration of some very elementary functions
Let be a natural number. Let and be real polynomials such that is not a square and has imaginary roots, if it is not linear. Effective methods for the integration of are exhibited.
Integration of the exponential function of a complex quadratic form.
Integrodifferential equations on time scales with Henstock-Kurzweil-Pettis delta integrals.
Integrodifferential inequality for stability of singularly perturbed impulsive delay integrodifferential equations.
Interior sphere property of attainable sets and time optimal control problems
This paper studies the attainable set at time T>0 for the control system showing that, under suitable assumptions on f, such a set satisfies a uniform interior sphere condition. The interior sphere property is then applied to recover a semiconcavity result for the value function of time optimal control problems with a general target, and to deduce C1,1-regularity for boundaries of attainable sets.
Intermediate values and inverse functions on non-Archimedean fields.
Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry.
We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general F-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide criteria for these Sobolev type inequalities and for related properties. In particular, we implement in the context of probability measures the ideas of Maz'ja's capacity theory, and present equivalent forms relating the capacity of sets to their measure. Orlicz hypercontractivity efficiently describes the...
Interpolating bases for spaces of differentiable functions
Interpolation and extrapolation of smooth functions by linear operators.
Interpolation and the Laguerre-Pólya class.
Interpolation Gevrey dans les domaines de type fini de C2.
Interval linear regression analysis based on Minkowski difference – a bridge between traditional and interval linear regression models
In this paper, we extend the traditional linear regression methods to the (numerical input)-(interval output) data case assuming both the observation/measurement error and the indeterminacy of the input-output relationship. We propose three different models based on three different assumptions of interval output data. In each model, the errors are defined as intervals by solving the interval equation representing the relationship among the interval output, the interval function and the interval...
Introduction to Rational Functions
In this article we formalize rational functions as pairs of polynomials and define some basic notions including the degree and evaluation of rational functions [8]. The main goal of the article is to provide properties of rational functions necessary to prove a theorem on the stability of networks
Introduction to the volume