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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
Dyadic Riesz Wavelets on Local Fields of Positive Characteristics
Author(s):
Kartik Garg, Raj Kumar, Satyapriya
Department of Mathematics,
University of Delhi,
Delhi,
India.
kartikgarg1421@gmail.com,
rajkmc@gmail.com
kmc.satyapriya@gmail.com
Abstract:
In this research paper, we introduce a novel theory for the construction of a Riesz wavelet basis in the space L2(K), where K is a local field with positive characteristics. Our approach is two fold: firstly, we derive some essential characterizations of the scaling function associated with the structure of a Riesz MRA on a local field, and secondly, we review existing methods for constructing wavelet frames in L2(K). We also present a well elaborated example for a better comprehension of our theory. Due to mathematical convenience, we limit ourselves to the case of dyadic dilations only.
Paper's Title:
The ε-Small Ball Drop Property
Author(s):
C. Donnini and A. Martellotti
Dipartimento
di Statistica e Matematica per la Ricerca Economica,
Universitŕ degli Studi di Napoli "Parthenope",
Via Medina, 80133 Napoli,
Italy
chiara.donnini@uniarthenope.it
{Dipartimento di Matematica e Informatica,
Universitŕ degli Studi di Perugia,
Via Pascoli - 06123 Perugia,
Italy.
amart@dipmat.unipg.it
URL:
www.dipmat.unipg.it/~amart/
Abstract:
We continue the investigation on classes of small sets in a
Banach space that give alternative formulations of the Drop
Property. The small sets here considered are the set having the
small ball property, and we show that for sets having non-empty
intrinsic core and whose affine hull contains a closed affine space
of infinite dimension the Drop Property can be equivalently
formulated in terms of the small ball property.
Paper's Title:
Maximal Singular Operators On Variable Exponent Sequence Spaces and Their Corresponding Ergodic Version
Author(s):
Sri Sakti Swarup Anupindi and Michael A. Alphonse
Department of Mathematics, Birla Institute
of Technology And Science- Pilani,
Hyderabad Campus, Jawahar Nagar, Kapra Mandal,
District.-Medchal-500 078 Telangana,
India.
E-mail:
p20180442@hyderabad.bits-pilani.ac.in
alphonse@hyderabad.bits-pilani.ac.in
URL:
https://www.bits-pilani.ac.in/hyderabad/a-michael-alphonse
https://www.bits-pilani.ac.in/research_scholars/sri-sakti-swarup-anupindi
Abstract:
In this paper, we prove strong and weak type inequalities of singular operators on weighted lwp(Z)$. Using these results, we prove strong type and weak type inequalities of the maximal singular operator of Calderon-Zygmund type on variable exponent sequence spaces lp(·)(Z). Using the Calderon-Coifman-Weiss transference principle, we prove strong type, weak type inequalities of the maximal ergodic singular operator on Lwp(X,B,μ) spaces, where (X,B,μ) is a probability space equipped with measure preserving transformation U.
Paper's Title:
Existence Results for Second Order Impulsive Functional Differential Equations with Infinite Delay
Author(s):
M. Lakrib, A. Oumansour and K. Yadi
Laboratoire de Mathématiques, Université Djillali
Liabées, B.P. 89 Sidi Bel Abbčs 22000, Algérie
mlakrib@univ-sba.dz
oumansour@univ-sba.dz
Laboratoire de Mathématiques, Université Abou Bekr
Belkaid, B.P. 119 Tlemcen 13000, Algérie
k_yadi@mail.univ-tlemcen.dz
Abstract:
In this paper we study the existence of solutions for second order impulsive functional differential equations with infinite delay. To obtain our results, we apply fixed point methods.
Paper's Title:
The boundedness of Bessel-Riesz operators on generalized Morrey spaces
Author(s):
Mochammad Idris, Hendra Gunawan and Eridani
Department of Mathematics,
Bandung Institute of Technology,
Bandung 40132,
Indonesia.
E-mail:
mochidris@students.itb.ac.id
Department of Mathematics,
Bandung Institute of Technology,
Bandung 40132,
Indonesia.
E-mail: hgunawan@math.itb.ac.id
URL:
http://personal.fmipa.itb.ac.id/hgunawan/
Department of Mathematics,
Airlangga University,
Surabaya 60115,
Indonesia.
E-mail: eridani.dinadewi@gmail.com
Abstract:
In this paper, we prove the boundedness of Bessel-Riesz operators on generalized Morrey spaces. The proof uses the usual dyadic decomposition, a Hedberg-type inequality for the operators, and the boundedness of Hardy-Littlewood maximal operator. Our results reveal that the norm of the operators is dominated by the norm of the kernels.
Paper's Title:
Commutator For Singular Operators On Variable Exponent Sequence Spaces And Their Corresponding Ergodic Version
Author(s):
A.M. Alphonse and S.S.S. Anupindi
Department of Mathematics,
Birla Institute of Technology And Science- Pilani,
Hyderabad Campus, Jawahar Nagar, Kapra Mandal,
District.-Medchal-500 078, Telangana,
India.
E-mail:
alphonse@hyderabad.bits-pilani.ac.in
p20180442@hyderabad.bits-pilani.ac.in
URL:
https://www.bits-pilani.ac.in/hyderabad/a-michael-alphonse
https://www.bits-pilani.ac.in/research_scholars/sri-sakti-swarup-anupindi
Abstract:
In this paper, we prove strong type inequality for maximal commutator of singular operator on weighted lp spaces. Using these results we prove strong type inequality for the maximal commutator of singular operator on variable exponent sequence spaces. Using Calderon-Coifman-Weiss transference principle we prove strong type inequality for maximal ergodic commutator of singular operator on a probability space equipped with measure preserving transformation U.
Paper's Title:
On Saturation of Norm Convergence of Walsh-Fourier Matrix Transform Means
Author(s):
István Blahota
Institute of Mathematics and Computer Sciences,
University of Nyíregyháza,
H-4400 Nyíregyháza,
Sóstói street 31/b,
Hungary
E-mail: blahota.istvan@nye.hu
Abstract:
In this paper we investigate the saturation of norm convergence issues for regular matrix transform means in case of Walsh-Paley system. The main result is the observation of equality ||σTn (f) - f ||p=0(a)n where an sequence of positive numbers tends to zero and there exists constant $c$, for which t1,n≤ can for every n∈P.
Paper's Title:
A Review on Minimally Supported Frequency Wavelets
Author(s):
K Pallavi1, M C Lineesh1, A Noufal2
1
Department of Mathematics,2Department of Mathematics,
Cochin University of Science and Technology,
Kerala 682022,
India.
E-mail: noufal@cusat.ac.in
Abstract:
This paper provides a review on Minimally Supported Frequency (MSF) wavelets that includes the construction and characterization of MSF wavelets. The characterization of MSF wavelets induced from an MRA is discussed and the nature of the low-pass filter associated with it is explained. The concept of wavelet set and dimension function is introduced to study this class of wavelets. Along with MSF wavelets, s-elementary wavelets and unimodular wavelets are also considered due to the similarity in definitions. Examples and illustrations are provided for more clarity.
Paper's Title:
The Projective Riccati Equations Method for Solving Nonlinear Schrodinger Equation in Bi-Isotropic Fiber
Author(s):
A. Ourahmoun, Z. Mezache
Optics and Precision Mechanics
Institute of Setif,
Algeria.
E-mail:
abbes.ourahmoun@univ-setif.dz
zinemezaache@yahoo.fr
Abstract:
Bi-isotropic materials, characterized by their chiral and non-reciprocal nature, present unique challenges and opportunities in scientific research, driving the development of cutting-edge applications. In this paper, we explore the influence of chirality using a newly developed framework that emphasizes the nonlinear effects arising from the magnetization vector under a strong electric field. Our research introduces a novel formulation of constitutive relations and delves into the analysis of solutions for the nonlinear Schr\"{o}dinger equation, which governs pulse propagation in nonlinear bi-isotropic media. By employing the Projective Riccati Equation Method with variable dispersion and nonlinearity, we systematically derive families of solutions to the nonlinear Schr\"{o}dinger equation in chiral and non-reciprocal optical fibers. This approach provides valuable insights into the propagation of light in two polarization modes right circularly polarized (RCP) and left circularly polarized (LCP) each associated with distinct wave vectors in nonlinear bi-isotropic environments. The study presents several new exact solutions of optical solitons within these media.
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