Analysis and Mathematical Physics

Abstract Given any compact Hausdorff space X , we present a simple proof that a continuous function $$g\in \mathcal {C}(X)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>C</mml:mi> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> can be uniformly approximated on X by elements of some linear subsp…

Abstract We study the deformation of the classical Szegő curve $$\gamma _0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>γ</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> given by $$\gamma _t = \{ z\in \mathbb {C}: |z\, e^{1-z}| = e^{-t}, |z|\le 1\}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>t</…

Abstract Let $$\mathcal {S}^*(\alpha _1,\alpha _2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mo>∗</mml:mo> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>α</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>α</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>)</mml:mo> </m…

Abstract This paper focuses on the study of multiplicity and localized concentration properties of positive solutions for the following singularly perturbed double phase problem with nonlocal Choquard reaction $$\begin{aligned} \left\{ \begin{array}{ll} -\epsilon ^{p}\Delta _{p} u-\epsilon ^{q}\Delta _{q} u +V(x)(|u|^{p-2}u+|u|^{q-2}u)\\ \quad =\epsilon ^{\mu -N}\left( \frac{1}{|x|^{\mu }}*G(u)\r…

Abstract Two interesting phenomena for the construction of quantum states are that of mutually unbiased bases and that of balanced states. We explore a constructive approach to each phenomenon that involves orthogonal polynomials on the unit circle. In the case of mutually unbiased bases, we show that this approach does not produce such bases. In the case of balanced states, we provide examples o…