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Todor D. Todorov
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Professor of Mathematics
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About Todor D. Todorov
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Professor of Mathematics,
California Polytechnic State University, San Luis Obispo
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Disciplines
Mathematics
Research Interests
Non-Linear Theory of Generalized Functions (Colombeau's Algebras), Non-Standard Analysis, Foundation of Quantum Mechanics
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Mathematics, Cal Poly
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Articles
Conference Proceedings
Articles
(22)
Article
An axiomatic approach to the non-linear theory of generalized functions ...
Integral Transforms and Special Functions (2011)
Todor D. Todorov
We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra ...
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Article
Completeness of the Leibniz Field and Rigorousness of Infinitesimal Calculus
ArvixMathematics (2011)
James F. Hall and Todor D. Todorov
We present a characterization of the completeness of the field of real numbers in the form of a collection of ...
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Article
Another Proof of the Existence a Dedekind Complete Totally Ordered ...
ArvixMathematics (2011)
James F. Hall and Todor D. Todorov
We describe the Dedekind cuts explicitly in terms of non-standard rational numbers. This leads to another construction of a Dedekind ...
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Article
Full algebra of generalized functions and non-standard asymptotic analysis
Logic and Analysis (2008)
Todor D. Todorov and Hans Vernaeve
We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions. We offer ...
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Article
A Lost Theorem: Definite Integrals in An Asymptotic Setting
The American Mathematical Monthly (2008)
Ray Cavalcante and Todor D. Todorov
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Article
Lecture Notes: Non-Standard Approach to J.F. Colombeau’s Theory ...
ArvixMathematics (2006)
Todor D. Todorov
In these lecture notes we present an introduction to non-standard analysis especially written for the community of mathematicians, physicists and ...
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Article
Existence and uniqueness of
v
-asymptotic expansions and Colombeau’s ...
Journal of Mathematical Analysis and Applications (2005)
Todor D. Todorov
We define a type of generalized asymptotic series called v-asymptotic. We show that every function with moderate growth at infinity ...
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Article
Radius of convergence of a power series
International Journal of Mathematical Education in Science and Technology (2003)
Todor D. Todorov
We derive two simple and memorizable formulas for the radius of convergence of a power series which seem to be ...
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Article
Back to Classics: Teaching Limits Through Infinitesimals
International Journal of Mathematical Education in Science and Technology (2001)
Todor D. Todorov
The usual ϵ, δ-definition of the limit of a function (whether presented at a rigorous or an intuitive level) requires ...
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Article
Nonstandard Analysis in Topology: Nonstandard and Standard Compactifications
Journal of Symbolic Logic (2000)
S. Salbany and Todor D. Todorov
Let (X, T) be a topological space, and ∗X a non–standard extension of X. There is a natural “standard” topology ...
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Article
An Embedding of Schwartz Distributions in the Algebra of Asymptotic ...
International Journal of Mathematics and Mathematics Science (1998)
Michael Oberguggenberger and Todor D. Todorov
We present a solution of the problem of multiplication of Schwartz distributions by embedding the space of distributions into a ...
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Article
An Existence Result for Linear Partial Differential Equations with
C ...
Transactions of the American Mathematical Society (1996)
Todor D. Todorov
We prove the existence of solutions for essentially all linear partial differential equations with C∞-coefficients in an algebra of generalized ...
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Article
Monads and Realcompactness
Topology and its Applications (1994)
Sergio Salbany and Todor D. Todorov
We give a quantifier free characterization of realcompactness and ordered realcompactness in terms of monads. We also present simple proofs ...
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Article
Nonstandard and Standard Compactifications of Ordered Topological Spaces
Topology and its Applications (1992)
Sergio Salbany and Todor D. Todorov
We construct the Nachbin ordered compactification and the ordered realcompactification, a notion defined in the paper, of a given ordered ...
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Article
Operations with Distribution Vectors
Demonstratio Mathematica (1987)
Brian Fisher and Todor D. Todorov
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Article
Asymptotic Functions as Kernels of the Schwartz Distributions
Bulgarian Journal of Physics (1985)
Todor D. Todorov
Using a version of the sequential method we introduce a class of generalized functions called here "asymptotic functions''. This class ...
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Article
The Products
δn2(x), δ(x). X-n, ϴ(x). X-n ...
Bulgarian Journal of Physics (1985)
Todor D. Todorov
Several products like δn(x), δ(x)ϴ(x), δ(m)(x). X-n, ϴ(x). X-n, etc., where δ(x), ϴ(x), X-n, etc., are kernels of the corresponding ...
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Article
Asymptotic Functions and the Problem of Multiplication of Distributions
Bulgarian Journal of Physics (1981)
Todor D. Todorov
The asymptotic functions are a new type of generalized functions. But they are not functionals on some space of test-functions ...
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Article
Quasi-Extended Asymptotic Functions
Bulgarian Journal of Physics (1981)
Todor D. Todorov
The class F of "quasi-extended asymptotic functions" introduced in the present paper contains all extended asymptotic functions [8, (3.1)] (in ...
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Article
Asymptotic Numbers: I. Algebraic Properties
Bulgarian Journal of Physics (1980)
Todor D. Todorov
The set of asymptotic numbers A introduced in Refs. [1] and [3] is a system of generalized numbers including the ...
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Article
Asymptotic Numbers: II. Order Relation, Infinitesimals and Interval Topology
Bulgarian Journal of Physics (1980)
Todor D. Todorov
It has been shown in [8] that the set of asympototic numbers A is a system of generalized numbers including ...
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Article
Asymptotic Numbers: Algebraic Operations with Them
Serdica, Bulgaricae Mathematicae Publicationes (1976)
Christo Ya. Christov and Todor D. Todorov
The main subject of the present paper is to define the four algebraic operations - additions, subtraction, multiplication and division ...
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Conference Proceedings
(3)
Presentation
Pointwise Kernels of Schwartz Distributions
Proceedings of the American Mathematical Society (1992)
Todor D. Todorov
We show that Schwartz distributions have kernels in the class of the pointwise nonstandard functions.
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Presentation
A Nonstandard Delta Function
Proceedings of the American Mathematical Society (1990)
Todor D. Todorov
We prove that the Dirac delta distribution has a kernel in the class of the pointwise nonstandard functions.
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Presentation
Alexander's Subbase Lemma
Proceedings of the American Mathematical Society (1989)
Todor D. Todorov and S. Salbany
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