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By
Gauthier, Paul; Zhu, Changzhong
In this paper we prove two properties of the weighted Hardy space for the unit disc with the weight function satisfying the Muckenhoupt condition.
By
Duyunova, Anna; Lychagin, Valentin; Tychkov, Sergey
Algebras of symmetries and the corresponding algebras of differential invariants for plane flows of inviscid fluids are given. Their dependence on thermodynamical states of media are studied and a classification of thermodynamical states is given.
By
Tu, Qiang ; Huang, Guangyue
We consider how mdimensional BakryÉmery Ricci curvature affects the geometry of the boundary
$$\partial M$$
. By using the Reilly’s formula with respect to fLaplacian, geometric inequalities involving fmean curvature are obtained. Furthermore, we also achieve the relationship between fmean curvature of the boundary submanifold and the mean curvature of submanifold
$$x:\partial M\rightarrow \mathbb {R}^N(c)$$
into space form
$$\mathbb {R}^N(c)$$
.
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By
Yurko, V.
1 Citations
We study inverse spectral problems for ordinary differential equations on compact startype graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the socalled Weyltype matrices which are generalizations of the Weyl function (mfunction) for the classical Sturm–Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.
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By
Arefijamaal, Ali Akbar; Ghaani Farashahi, Arash
9 Citations
Let
$$H$$
be a locally compact group and
$$K$$
be an LCA group also let
$$\tau :H\rightarrow Aut(K)$$
be a continuous homomorphism and
$$G_\tau =H\ltimes _\tau K$$
be the semidirect product of
$$H$$
and
$$K$$
with respect to
$$\tau $$
. In this article we define the Zak transform
$$\mathcal{Z }_L$$
on
$$L^2(G_\tau )$$
with respect to a
$$\tau $$
invariant uniform lattice
$$L$$
of
$$K$$
and we also show that the Zak transform satisfies the Plancherel formula. As an application we analyze how these technique apply for the semidirect product group
$$\mathrm SL (2,\mathbb{Z })\ltimes _\tau \mathbb{R }^2$$
and also the WeylHeisenberg groups.
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By
Fenton, P. C.; Rossi, John
Suppose that
$$u$$
is subharmonic in the plane and such that, for some
$$c>1$$
and sufficiently large
$$K_0=K_0(c)$$
,
$$u$$
is harmonic in the disc
$$\Delta (z,\tau (z)^{c})$$
whenever
$$u(z)>B(z,u)K_0\log \tau (z)$$
, where
$$\tau (z)=\max \{z,B(z,u)\}$$
and
$$B(r,u)=\max _{z=r}u(z)$$
. It is shown that if in addition
$$u$$
satisfies a certain lower growth condition, then there are ‘Wiman–Valiron discs’ in each of which
$$u$$
is the logarithm of the modulus of an analytic function, and that the derivatives of the analytic functions have regular asymptotic growth.
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By
Liu, Yu; Dong, Huanhe; Zhang, Yong
13 Citations
From the isospectral problem which we design, a
$$(1+1)$$
dimensional discrete integrable hierarchy is generated with the help of a loop algebra. After that we get a differential–difference integrable system with two potential functions. Finally, the algebrogeometric solution of the integrable system is obtained by straightening out the continuous and discrete flow and utilizing the Riemann–Jacobi inversion theorem.
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By
Gumenyuk, Pavel; Prause, István
Becker (J Reine Angew Math 255:23–43, 1972) discovered a sufficient condition for quasiconformal extendibility of Loewner chains. Many known conditions for quasiconformal extendibility of holomorphic functions in the unit disk can be deduced from his result. We give a new proof of (a generalization of) Becker’s result based on Slodkowski’s Extended
$$\lambda $$
Lemma. Moreover, we characterize all quasiconformal extensions produced by Becker’s (classical) construction and use that to obtain examples in which Becker’s extension is extremal (i.e. optimal in the sense of maximal dilatation) or, on the contrary, fails to be extremal.
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