We establish an explicit Plancherel decomposition for
GL
n
(
F
)
\
GL
n
(
E
)
where
E
/
F
is a quadratic extension of local fields of characteristic zero by making use of a local functional equation ...for Asai
γ
-factors. We also give two applications of this Plancherel formula: first to the global Ichino–Ikeda conjecture for unitary groups by completing a comparison between local relative characters that was left open by Zhang (J Am Math Soc 27:541–612, 2014) and secondly to the Hiraga–Ichino–Ikeda conjecture on formal degrees (J Am Math Soc 21(1):283–304, 2008) in the case of unitary groups.
Yang–Mills theories are an important building block of the standard model and in particular of quantum chromodynamics. Its correlation functions describe the behavior of its elementary particles, the ...gauge bosons. In quantum chromodynamics, the correlation functions of the gluons are basic ingredients for calculations of hadrons from bound state equations or properties of its phase diagram with functional methods.
Correlation functions of gluons are defined only in a gauge fixed setting. The focus of many studies is the Landau gauge which has some features that alleviate calculations. I discuss recent results of correlation functions in this gauge obtained from their equations of motions. Besides the four-dimensional case also two and three dimensions are treated, since the effects of truncations, viz., the procedure to render the infinitely large system of equations finite, can be studied more directly in these cases. In four dimensions, the anomalous running of dressing functions plays a special role and it is explained how resummation is realized in the case of Dyson–Schwinger equations.
Beyond the Landau gauge other gauges can provide additional insights or can alleviate the development of new methods. Some aspects or ideas are more easily accessible in alternative gauges and the results presented here for linear covariant gauges, the Coulomb gauge and the maximally Abelian gauge help to refine our understanding of Yang–Mills theories.
Stability of an non-additive functional equation Govindan, Vediyappan; Gunasekaran, Nallappan; Pinelas, Sandra
Journal of physics. Conference series,
07/2020, Letnik:
1597, Številka:
1
Journal Article
Recenzirano
Odprti dostop
In this paper, the authors investigated the general solution and generalized Hyers-Ulam stability of Non additive functional equation of the form Ω(2θ1±θ2±θ3) + 2Ω(θ2) + 2Ω(θ3) = 2Ω(θ1±θ2) + ...2Ω(θ1±θ3) + Ω(θ2±θ3) in Banch space using direct and fixed point methods.
Extended versions of the Bourgain-Brezis-Mironescu theorems on the limit as s right arrow 1.sup.- of the Gagliardo-Slobodeckij fractional seminorm are established in the Orlicz space setting. Our ...results hold for fractional Orlicz--Sobolev spaces built upon general Young functions, and complement those of 13, where Young functions satisfying the DELTA.sub.2 and the nabla.sub.2 conditions are dealt with. The case of Young functions with an asymptotic linear growth is also considered in connection with the space of functions of bounded variation. KEY WORDS: Fractional Orlicz--Sobolev spaces, limit of smoothness parameters, Orlicz--Sobolev spaces, functions of bounded variation MATHEMATICS SUBJECT CLASSIFICATION: 46E35, 46E30
In this paper, we solve the system of functional equations
{
f
(
x
+
y
)
+
g
(
y
−
x
)
=
2
f
(
x
)
,
g
(
x
+
y
)
−
f
(
y
−
x
)
=
2
g
(
y
)
and we investigate the stability of
g
-derivations in Banach ...algebras.
On a new class of fractional operators Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet ...
Advances in difference equations,
08/2017, Letnik:
2017, Številka:
1
Journal Article
Recenzirano
Odprti dostop
This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces ...and present some theorems related to these operators.
We introduce and discuss the concept of n-ary K-increasing fusion functions and n-ary K-increasing aggregation functions, K being a subset of the index set {1,…,n} indicating in which variables a ...considered function is increasing. It is also assumed that this function is decreasing in all other variables. We show that each n-ary K-increasing aggregation function is generated by some aggregation function which enables us to introduce and study the properties of n-ary K-increasing aggregation functions related to the properties of their generating aggregation functions. In particular, we also discuss binary K-increasing aggregation functions, including fuzzy implication and complication functions, among others.
Celotno besedilo
Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
This is a completely revised English edition of the important Analyse fonctionnelle (1983). It contains a wealth of problems and exercises to guide the reader. It is also the first single-volume ...textbook to cover related fields of functional analysis and PDEs.
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.
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