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Wiley
The L2‐norm of the Cauchy transform on circular annuli
Abstract We compute the exact operator norm of the Cauchy transform on a circular annulus . Exploiting rotational symmetry and a Fourier mode decomposition, we reduce the problem to a one‐dimensional weighted Hardy operator and obtain where is the first eigenvalue of the Laplacian on with Neumann condition on the inner boundary and Dirichlet condition on the outer boundary....
Download 2026 David Kalaj
Cambridge University Press (CUP)
Isoperimetric inequality for nearly spherical domains in the Bergman ball double struck upper B 2$\mathbb{B}_2$ 𝔹 2
We prove a quantitative isoperimetric inequality for nearly spherical domains in the Bergman ball in double struck upper C 2 $\mathbb{C}^2$ ℂ 2...
Download 2026 David Kalaj
Wiley
The radial symmetry of minimizers to the p$p$ weighted Dirichlet energy in R3$\mathbb {R}^3$
AbstractLet and be annuli in . Let , and assume that is the class of Sobolev homeomorphisms of onto . Then, we consider the following Dirichlet‐type energy of : We prove that this energy integral attains its minimum for and , and the minimum is a certain radial diffeomorphism .For general , we minimize the Dirichlet‐type integral throughout the class of radial mappings between given annuli, and this minimum always exists for . For , the image annulus cannot be too thick, which is opposite...
Download 2024 David Kalaj
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