A5009332670- Advanced Harmonic Analysis Research
- Advanced Banach Space Theory
- Differential Equations and Boundary Problems
- Mathematical functions and polynomials
- Holomorphic and Operator Theory
- Mathematical Analysis and Transform Methods
- Algebraic and Geometric Analysis
- advanced mathematical theories
- Advanced Mathematical Modeling in Engineering
- Fixed Point Theorems Analysis
- Approximation Theory and Sequence Spaces
- Numerical methods in inverse problems
- Advanced Topics in Algebra
- Fractional Differential Equations Solutions
- Nonlinear Differential Equations Analysis
- Advanced Algebra and Geometry
- Spectral Theory in Mathematical Physics
- Scientific Research and Discoveries
- Differential Equations and Numerical Methods
- Historical and socio-economic studies of Spain and related regions
- Matrix Theory and Algorithms
- Finite Group Theory Research
- Advanced Mathematical Physics Problems
- Optimization and Variational Analysis
- Mathematical and Theoretical Analysis
Benemérita Universidad Autónoma de Puebla
2011-2024
<abstract><p>We construct the Henstock-Kurzweil (HK) integral as an extension of a linear form initially defined on $ L^{1} $, but which is not continuous in this space. This gives us alternative way to prove existing results. In particular, we give new characterization dual space integrable functions terms quotient space.</p></abstract>
We consider the Fourier transform in space of Henstock-Kurzweil integrable functions. prove that classical results related to Riemann-Lebesgue lemma, existence and continuity are true appropriate subspaces.
We show conditions for the existence, continuity, and differentiability of functions defined by , where is a function bounded variation on with .
<p style='text-indent:20px;'>In this paper, we generalize the Riemann-Liouville differential and integral operators on space of Henstock-Kurzweil integrable distributions, <inline-formula><tex-math id="M1">$ D_{HK} $</tex-math></inline-formula>. We obtain new fundamental properties fractional derivatives integrals, a general version theorem calculus, semigroup property for relations between operators. Also, achieve generalized characterization solution Abel...
Employing an isometrically isomorphic space, we determine new properties for the completion of space Henstock-Kurzweil integrable functions with Alexiewicz norm.
In this work we study the Cosine Transform operator and Sine in setting of Henstock-Kurzweil integration theory. We show that these related transformation operators have a very different behavior context functions. fact, while one them is bounded operator, other not. This generalization result E. Liflyand Lebesgue integration.
In this paper we prove the Convolution Theorem for Fourier Integral transform over a subset of bounded variation functions which vanish at infinity.This is dense in L 2 (R) .Moreover, it does not have inclusion relations with space Lebesgue integrable functions.We employ Henstock-Kurzweil integral.
Employing the Henstock-Kurzweil integral, we make simple proofs of Riemann-Lebesgue lemma and Dirichlet-Jordan theorem for functions bounded variation which vanish at infinity.
We show that if f is lying on the intersection of space Henstock-Kurzweil integrable functions and bounded variation in neighborhood ± ∞, then its Fourier Transform exists all R. This result more general than classical which enunciates Lebesgue integrable, R, because we also have proved there are belong to not integrable.
In this paper we show the Jordan decomposition for bounded variation functions with values in Riesz spaces. Through an equivalence relation, prove that is satisfied valued Hilbert This result a generalization of real case. Moreover, that, general, not vector-valued functions.
This work proves pointwise convergence of the truncated Fourier double integral non-Lebesgue integrable bounded variation functions. leads to Dirichlet-Jordan theorem proof for functions, which has not been sufficiently studied. Note that recent contributions regarding this subject consider Lebesgue [F. Moricz, 2015], [B. Ghodadra-V. Fuulop, 2016].
<p>In this paper, the convergence of spectral parameter power series method, proposed by Kravchenko, is performed for Sturm–Liouville equation with Kurzweil–Henstock integrable coefficients. Numerical simulations some examples are also presented to validate performance method.</p>