Results 11 to 20 of about 602 (89)
On Products of Distributions in Colombeau Algebra [PDF]
Mathematical Problems in Engineering, 2014 Results on products of distributions and δ(p)(x) are derived. They are obtained in Colombeau differential algebra 𝒢(R) of generalized functions that contains the space 𝒟′(R) of Schwartz distributions as a subspace. Products of this form are useful in quantum renormalization theory in Physics.
Miteva, Marija +2 more
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Colombeau algebras without asymptotics. [PDF]
J Pseudodiffer Oper Appl, 2019 22 ...
Nigsch EA.
europepmc +6 more sources
Isomorphisms of algebras of Colombeau generalized functions
, 2006 We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X.
A. Delcroix +25 more
core +2 more sources
International Journal of Differential Equations, Volume 2023, Issue 1, 2023., 2023 This manuscript aims to highlight the existence and uniqueness results for the following Schrödinger problem in the extended Colombeau algebra of generalized functions. 1/ı∂/∂tut,x−△ut,x+vxut,x=0,t∈R+,x∈Rn,vx=δx,u0,x=δx, where δ is the Dirac distribution. The proofs of our main results are based on the Gronwall inequality and regularization method.
Ali El Mfadel +4 more
wiley +1 more source
Full and Special Colombeau Algebras [PDF]
Proceedings of the Edinburgh Mathematical Society, 2018 AbstractWe introduce full diffeomorphism-invariant Colombeau algebras with addedε-dependence in the basic space. This unites the full and special settings of the theory into one single framework. Using locality conditions we find the appropriate definition of point values in full Colombeau algebras and show that special generalized points suffice to ...
Nigsch, Eduard, Grosser, Michael
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On a wave equation with singular dissipation
Mathematische Nachrichten, Volume 295, Issue 8, Page 1591-1616, August 2022., 2022 Abstract In this paper we consider a singular wave equation with distributional and more singular non‐distributional coefficients and develop tools and techniques for the phase‐space analysis of such problems. In particular we provide a detailed analysis for the interaction of singularities of solutions with strong singularities of the coefficient in a
Mohammed Elamine Sebih, Jens Wirth
wiley +1 more source
The category of Colombeau algebras [PDF]
Monatshefte für Mathematik, 2016 In [11], we introduced the notion of asymptotic gauge (AG), and we used it to construct Colombeau AG-algebras. This construction concurrently generalizes that of many different algebras used in Colombeau's theory, e.g. the special one $\mathcal{G}^{\srm}$, the full one $\gse$, the NSA based algebra of asymptotic functions $\hat{\mathcal{G}}$, and the ...
Luperi Baglini, Lorenzo, Giordano, Paolo
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Unifying order structures for Colombeau algebras [PDF]
Mathematische Nachrichten, 2014 We define a general notion of set of indices which, using concepts from pre-ordered sets theory, permits to unify the presentation of several Colombeau-type algebras of nonlinear generalized functions. In every set of indices it is possible to generalize Landau's notion of big-O such that its usual properties continue to hold.
Giordano, Paolo, Nigsch, Eduard
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Introducing the γ function in quantum theory
International Journal of Quantum Chemistry, Volume 120, Issue 13, July 1, 2020., 2020 The existence of the square‐root of the Dirac's delta function is postulated. When it is used to construct wave functions, it turns out to be useful to construct a theory between classical and quantum mechanics: it uses quantum formulation (operators, wave functions, expectation values) but it can describe classical situations such as a particle at ...
Péter R. Surján
wiley +1 more source
Asymptotic gauges: Generalization of Colombeau type algebras [PDF]
Mathematische Nachrichten, 2015 We use the general notion of set of indices to construct algebras of nonlinear generalized functions of Colombeau type. They are formally defined in the same way as the special Colombeau algebra, but based on more general “growth condition” formalized by the notion of asymptotic gauge.
Giordano P., Luperi baglini L.
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