In this research paper, we deal with the problem of determining the function χ:G→R, which is the solution to the maximum functional equation (MFE) max{χ(xy),χ(xy−1)}=χ(x)χ(y), when the domain is a ...discretely normed abelian group or any arbitrary group G. We also analyse the stability of the maximum functional equation max{χ(xy),χ(xy−1)}=χ(x)+χ(y) and its solutions for the function χ:G→R, where G be any group and also investigate the connection of the stability with commutators and free abelian group K that can be embedded into a group G.
The goal of this paper is to provide a complete and refined study of the standard
L
-functions
L
(
π
,
Std
,
s
)
for certain non-generic cuspidal automorphic representations
π
of
G
2
(
A
)
. For a ...cuspidal automorphic representation
π
of
G
2
(
A
)
that corresponds to a modular form
φ
of level one and of even weight on
G
2
, we explicitly define the completed standard
L
-function,
Λ
(
π
,
Std
,
s
)
. Assuming that a certain Fourier coefficient of
φ
is nonzero, we prove the functional equation
Λ
(
π
,
Std
,
s
)
=
Λ
(
π
,
Std
,
1
-
s
)
. Our proof proceeds via a careful analysis of a Rankin-Selberg integral that is due to an earlier work of Gurevich and Segal.
As a powerful tool for models of quantum computing, q-calculus has drawn the attention of many researchers in the discipline of special functions. In this paper, we present new properties and ...characterize q-Bessel functions of the first kind using some identities of q-calculus. The results presented in this article help us to obtain new expression results related to q-special functions. New summation and integral representations for q-Bessel functions of the first kind are also established. A few examples are also provided to demonstrate the effectiveness of the proposed strategy.
An algebraic characterization of B-splines Kamont, Anna; Passenbrunner, Markus
Journal of mathematical analysis and applications,
08/2023, Letnik:
524, Številka:
1
Journal Article
Recenzirano
B-splines of order k can be viewed as a mapping N taking a (k+1)-tuple of increasing real numbers a0<⋯<ak and giving as a result a certain piecewise polynomial function. Looking at this mapping N as ...a whole, basic properties of B-spline functions imply that it has the following algebraic properties: (1) N(a0,…,ak) has local support contained in the interval a0,ak; (2) N(a0,…,ak) allows refinement, i.e. for every a∈∪j=0k−1(aj,aj+1) we have that if (α0,…,αk+1) is the increasing rearrangement of the points {a0,…,ak,a}, the ‘old’ function N(a0,…,ak) is a linear combination of the ‘new’ functions N(α0,…,αk) and N(α1,…,αk+1); (3) N is translation and dilation invariant. It is easy to see that derivatives of N(a0,…,ak) satisfy properties (1)–(3) as well.
Let F be a mapping taking (k+1)-tuples of increasing real numbers to some generalized function. In this paper we show that under some additional mild condition on the size of the supports of F(a0,…,ak) relative to the interval a0,ak, properties (1)–(3) are already sufficient to deduce that F(a0,…,ak) is a non-zero multiple of (some derivative of) a B-spline function. However, and somewhat surprisingly, we explicitly give examples of choices of F satisfying (1)–(3) but are not of this form.
This volume describes quantum wave equations in higher dimensions at an advanced level, placing all current mathematical and physical concepts and techniques at the reader's disposal. Readers will ...learn about quantum wave equations in higher dimensions and their broad range of applications.
In the present paper, the authors introduce and investigate two new subclasses of the function class B of bi-univalent analytic functions in an open unit disk U connected with a linear q-convolution ...operator. The bounds on the coefficients |csub.2 |,|csub.3 | and |csub.4 | for the functions in these new subclasses of B are obtained. Relevant connections of the results presented here with those obtained in earlier work are also pointed out.
By using the fractional Caputo–Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model ...by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.
We describe a method to compute mod Formula omitted Galois representations contained in the Formula omitted of surfaces. We apply this method to the case of a representation with values in Formula ...omitted attached to an eigenform over a congruence subgroup of Formula omitted. We obtain, in particular, a polynomial with Galois group isomorphic to the simple group Formula omitted and ramified at 2 and 3 only.
In this paper, we introduce a way of representing a given mapping as the sum of odd and even mappings. Then, using this representation, we investigate the stability of various forms of the following ...general nonic functional equation: ∑i=01010Ci(−1)10−if(x+iy)=0.
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