Operational calculus of linear unbounded operators and semigroups

1971 ◽  
Vol 4 (4) ◽  
pp. 290-298
Author(s):  
G. I. Laptev
Keyword(s):  
Operational Calculus ◽  
Unbounded Operators

scholarly journals A characterization of unbounded generalized meromorphic operators

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5421-5431
Author(s):  
Mohamed Berkani ◽  
Monia Boudhief ◽  
Nedra Moalla
Keyword(s):  
Finite Subset ◽  
Operational Calculus ◽  
Unbounded Operators ◽  
Neighborhood Theorem

In this paper, we study the class of unbounded generalized meromorphic operators GM(E,?), where E is a finite subset of C, which generalizes the notion of unbounded meromorphic operators. More precisely, we give a decomposition and some characterizing properties of these operators based on the punctured neighborhood theorem and the operational calculus for unbounded operators.

The Supersonic Flow Past a Slender Ducted Body of Revolution with an Annular Intake

1950 ◽  
Vol 1 (4) ◽  
pp. 305-318
Author(s):  
G. N. Ward
Keyword(s):  
Supersonic Flow ◽  
Velocity Potential ◽  
Operational Calculus ◽  
The Body ◽  
Body Of Revolution ◽  
Internal Flows ◽  
Flow Past ◽  
External Forces ◽  
Internal Pressures ◽  
Slender Body Of Revolution

SummaryThe approximate supersonic flow past a slender ducted body of revolution having an annular intake is determined by using the Heaviside operational calculus applied to the linearised equation for the velocity potential. It is assumed that the external and internal flows are independent. The pressures on the body are integrated to find the drag, lift and moment coefficients of the external forces. The lift and moment coefficients have the same values as for a slender body of revolution without an intake, but the formula for the drag has extra terms given in equations (32) and (56). Under extra assumptions, the lift force due to the internal pressures is estimated. The results are applicable to propulsive ducts working under the specified condition of no “ spill-over “ at the intake.

scholarly journals Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 354
Author(s):  
Alexander Apelblat ◽  
Francesco Mainardi
Keyword(s):  
Laplace Transform ◽  
Operational Calculus ◽  
Inverse Laplace Transform ◽  
Elementary Functions ◽  
Hyperbolic Functions ◽  
Error Functions ◽  
Convolution Integrals ◽  
Special Case ◽  
Integral Identities ◽  
Finite Integrals

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

scholarly journals Operational Calculus

Nature ◽  
1967 ◽  
Vol 215 (5099) ◽  
pp. 444-444
Author(s):  
A. ERDÉLYI
Keyword(s):  
Operational Calculus

Transients in Electric Circuits, Using the Heaviside Operational Calculus

1942 ◽  
Vol 26 (270) ◽  
pp. 149
Author(s):  
N. W. McAchlan ◽  
W. B. Coulthard
Keyword(s):  
Operational Calculus ◽  
Electric Circuits

scholarly journals Operational Calculus Approach to Nonlocal Cauchy Problems

2010 ◽  
Vol 4 (2-3) ◽  
pp. 243-258 ◽  
Author(s):  
Ivan Dimovski ◽  
Margarita Spiridonova
Keyword(s):  
Operational Calculus ◽  
Cauchy Problems
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