Displaying similar documents to “Practice of operator relationships in symbolical calculus.”

A new view of some operators and their properties in terms of the Non-Newtonian Calculus

Erdal Ünlüyol, Seren Salas, Imdat Iscan (2017)

Topological Algebra and its Applications

Similarity:

Differentiation and integration are basic operations of calculus and analysis. Indeed, they are in- finitesimal versions of substraction and addition operations on numbers, respectively. From 1967 till 1970 Michael Grossman and Robert Katz gave definitions of a new kind of derivative and integral, converting the roles of substraction and addition into division and multiplication, respectively and thus established a new calculus, called Non-Newtonian Calculus. So in this paper, it is...

Compact AC-operators

Ian Doust, Byron Walden (1996)

Studia Mathematica

Similarity:

We prove that compact AC-operators have a representation as a combination of disjoint projections which mirrors that for compact normal operators. We also show that unlike arbitrary AC-operators, compact AC-operators admit a unique splitting into real and imaginary parts, and that these parts must necessarily be compact.

A note on the convergence of partial Szász-Mirakyan type operators

Monika Herzog (2014)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Similarity:

In this paper we study approximation properties of partial modified Szasz-Mirakyan operators for functions from exponential weight spaces. We present some direct theorems giving the degree of approximation for these operators. The considered version of Szász-Mirakyan operators is more useful from the computational point of view.

Operational Methods in the Environment of a Computer Algebra System

Spiridonova, Margarita (2009)

Serdica Journal of Computing

Similarity:

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009. The presented research is related to the operational calculus approach and its representative applications. Operational methods are considered, as...

H ∞ functional calculus for an elliptic operator on a half-space with general boundary conditions

Giovanni Dore, Alberto Venni (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Let A be the L p realization ( 1 < p < ∞ ) of a differential operator P ( D x , D t ) on ℝ n × ℝ + with general boundary conditions B k ( D x , D t ) u ( x , 0 ) = 0 ( 1 ≤ k ≤ m ). Here P is a homogeneous polynomial of order 2 m in n + 1 complex variables that satisfies a suitable ellipticity condition, and for 1 ≤ k ≤ m B k is a homogeneous polynomial of order m k < 2 m ; it is assumed that the usual complementing condition is satisfied. We prove that A is a sectorial operator with a bounded H ∞ functional calculus.

Integral formulae for special cases of Taylor's functional calculus

D. Albrecht (1993)

Studia Mathematica

Similarity:

In this paper integral formulae, based on Taylor's functional calculus for several operators, are found. Special cases of these formulae include those of Vasilescu and Janas, and an integral formula for commuting operators with real spectra.