On the Foundations of Nonlinear Generalized Functions I
نویسندگان
چکیده
We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given. 2000 Mathematics Subject Classification. Primary 46F30; Secondary 26E15, 46E50, 35D05.
منابع مشابه
Institute for Mathematical Physics on the Foundations of Nonlinear Generalized Functions I on the Foundations of Nonlinear Generalized Functions I
We construct a diieomorphism invariant (Colombeau-type) diierential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing diierential calculus in innnite dimensional (convenient) vector spaces, previous attempts in this direction are uniied and completed. Several classiication results are achieved and applications to nonlinear diierential equations inv...
متن کاملApproximately generalized additive functions in several variables via fixed point method
In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability in random normed spaces, in non-Archimedean spaces and also in $p$-Banach spaces and finally the stability via fixed point method for a functional equationbegin{align*}&D_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1, i...
متن کاملOn the Distribution Functions of the Range and Quasi-range for the Extended Type I Generalized Logistic Distribution
In this paper, we obtain the distribution functions of the range and the quasi-range of the random variables arising from the extended type I generalized logistic distribution.
متن کاملOn generalized Hermite-Hadamard inequality for generalized convex function
In this paper, a new inequality for generalized convex functions which is related to the left side of generalized Hermite-Hadamard type inequality is obtained. Some applications for some generalized special means are also given.
متن کاملOn the foundations of nonlinear generalized functions II
This paper gives a comprehensive analysis of algebras of Colombeau-type generalized functions in the range between the diffeomorphism-invariant quotient algebra G = EM/N introduced in part I and Colombeau’s original algebra G . Three main results are established: First, a simple criterion describing membership in N (applicable to all types of Colombeau algebras) is given. Second, two counterexa...
متن کامل