Related papers: Real Analytic Generalized Functions

We consider a subanalytic subset A of a complex analytic manifold M (when M is viewed as a real manifold) and formulate conditions under which A is a complex analytic subset of M.

Ultrafunctions are a particular class of functions defined on a Non Archimedean field R^{*}\supset R. They have been introduced and studied in some previous works ([1],[2],[3]). In this paper we introduce a modified notion of ultrafunction…

We describe an abstract 2-categorical setting to study various notions of polynomial and analytic functors and monads.

We define the algebra of Colombeau generalized functions on the space of generalized points of {\mathbb R}^d which naturally contains the tempered generalized functions. The subalgebra of \mathscr{S}-regular generalized functions of this…

The main object of this paper is to study the generalized von mangoldt function using the L-additive function, which can help us give many result about the classical arithmetic function.

Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic…

Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…

The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the authors provide a general introduction to the umbral version of…

We introduce the notion of generalized function taking values in a smooth manifold into the setting of full Colombeau algebras. After deriving a number of characterization results we also introduce a corresponding concept of generalized…

In this article the algorithm for transformation of logic functions which are given by truth tables is considered. The suggested algorithm allows the transformation of many-valued logic functions with the required number of variables and…

We find an unifying approach to the analytic representation of the domain bounded by a generalized Pascal snail. Special cases as Pascal snail, Both leminiscate, conchoid of the Sluze and a disc are included. The behavior of functions…

An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

Geometric Quantization links holomorphic geometry with real geometry, a relation that is a prototype for the modern development of mirror symmetry. We show how to use this treatment to construct a special basis in every space of conformal…

We study various asymptotic approximations of Good's special functions arising in atomic physics. These special functions are situated beyond Anger's functions to which they are closely related. Our major tool is the method of the…

The authors survey recent results in special functions, particularly the gamma function and the Gaussian hypergeometric function.

An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…

Extending the work of Freese and Cook, which develop the basic theory of calculus and power series over real associative algebras, we examine what can be said about the logarithmic functions over an algebra. In particular, we find that for…

We prove local inequalities for analytic functions defined on a convex body in $\Re^{n}$ which generalize well-known classical inequalities for polynomials.

Let X be an affine real algebraic set . We investigate on the theory of algebraically constructible functions on X and the description of the semi-algebraic subsets of X when we replace the polynomial functions on X by some rational…