Growth properties of the q-Dunkl transform in the space $$L^{p}_{q,\alpha }({\mathbb {R}}_{q},|x|^{2\alpha +1}d_{q}x)$$ L q , α p ( R q , | x | 2 α + 1 d q x )

The Ramanujan Journal - Our aim in this work is to prove an analogue of Titchmarsh’s theorem [19, Theorem 84] and Younis’s theorem [20, Theorem 3.3] on the image under the q-Dunkl...     

On the exponential diophantine equation $$\left( am^{2}+1\right) ^{x}+\left( bm^{2}-1\right) ^{y}=(cm)^{z}$$ with $$ c\mid m $$c∣m

Let \(a,\ b,\ c,\ m\) be positive integers such that \(a+b=c^2, 2\mid a, 2\not \mid c\) and \(m>1\). In this paper we prove that if \(c\mid m \) and \(m>36c^3 \log c\), then the equation \((am^2+1)^x+(bm^2-1)^y=(cm)^z\) has only the positive integer solution \((x,\ y,\ z)\)=\((1,\ 1,\ 2)\).     

A necessary condition for the completeness of the system \left\{ {e^{ - \lambda _n t} |Re\lambda _n > 0} \right\} in the spaces C 0(ℝ+) and L p (ℝ+), p > 2

We obtain a necessary condition for the completeness of the system $$ e(\Lambda ) = \left\{ {e^{ - \lambda _n t} |Re\lambda _n > 0,n \in \mathbb{Z}} \right\} $$ in the spaces C ₀ and L ^p (?₊), p > 2, for the case in which the set of limit points of the sequence {λ _n } is countable and separable.     

Hybrid subconvexity bounds for $$L(1/2,\hbox {sym}^{2} f \otimes \chi )$$ L ( 1 / 2 , sym 2 f ⊗ χ )

The Ramanujan Journal - Let $$k\ge 2$$ be an even integer, and let M be a positive integer. We prove a hybrid subconvexity bound for $$L(1/2,\text {sym}^2 f\otimes \chi )$$ with the associated...     

A necessary and sufficient condition for the biorthogonality of {ρ 1,ρ 2}

In this paper, we present a necessary and sufficient condition for the biorthogonality of a class of special functionsρ ₁ andρ ₂. The functions are useful in the theory of biorthogonal wavelet.     

Coincidence of the spaces\mathop {J_2^1 }\limits^ \circ (\Omega ) and for plane domains Ω, having exits at infinity

For a large class of plane domains Ω, having exits at infinity, one shows the coincidence of the spaces of solenoidal vector fields \(\mathop {J_2^1 }\limits^ \circ (\Omega )\) and , which play an important role in the investigation of initial-houndary-value problems for the Navier-Stokes equations.     

A Kähler structure for the $$\text {PU}(2, 1)$$ PU ( 2 , 1 ) configuration space of four points in $$S^3$$ S 3

Geometriae Dedicata - We show that an open subset $${\mathfrak {F}}_4''$$ of the $$\mathrm{PU}(2,1)$$ configuration space of four points in $$S^3$$ is in bijection with an open subset of...     

S-forcing IIa: Adding diamonds and more applications: Coding sets,Arhangel’skii’s problem and ℒ[Q_1^{< \omega } ,Q_2^1 ]

We continue our earlier paper [20] by proving the equivalence, for regularκ>ω, of the existence of (κ, 1) morasses with built-in ♦ sequences and a strengthening, S_K◊ , of the forcing principle, S_K◊ of [20]. We obtain various applications of S_K◊, to wit: the existence of a stationary subset of [K₊]_<K with sup as coding function, the existence of a counterexample to Arhangel’skii’s conjecture (κ=ℵ₁) and compactness, axiomatizability and transfer properties for the Magidor-Malitz language ℒ (κ=ℵ₁). Research partially supported by NSF Grant MCS 8301042.     

Recursion operators and hierarchies of $$text{mKdV}$$ equations related to the Kac–Moody algebras $$D_4^{(1)}$$ , $$D_4^{(2)}$$ , and $$D_4^{(3)}$$

Theoretical and Mathematical Physics - We construct three nonequivalent gradings in the algebra $$D_4simeq so(8)$$ . The first is the standard grading obtained with the Coxeter automorphism...