The zeros of semi-orthogonal functions with respect to a probability measure µ supported on the unit circle can be applied to obtain Szeg˝ o quadrature formulas. The discrete measures generated by these formulas weakly converge to the orthogonality measure µ. In this paper we construct families of semi-orthogonal functions with interlacing zeros, and give a representation of the support of µ in...

The definition of classical holomorphic function spaces such as the Hardy space or Dirichlet on Hartogs triangle is not canonical. In this paper we introduce a natural family which includes some weighted Bergman spaces, candidate and space. For study L p mapping properties Szeg? projection respectively, whereas for prove it isometric to bidisc.

In the current work, we use (M,N)-Lucas Polynomials to introduce a new family of holomorphic and bi-univalent functions which involve linear combination between Bazilevic ?-pseudo-starlike function defined in unit disk D establish upper bounds for second third coefficients belongs this family. Also, discuss Fekete-Szeg? problem

In this investigation, the q-difference operator and S?l?gean q-differential are utilized to establish novel subclasses of analytical bi-close-to-convex functions. We determine general Taylor–Maclaurin coefficient functions in class using Faber polynomial method. demonstrate unpredictable behaviour initial coefficients a2, a3 investigate Fekete–Szeg? problem a3?a22 for To highlight connections ...

We investigate spectral features of the Dirac operator with infinite mass boundary conditions in a smooth bounded domain $\mathbb{R}^2$. Motivated by geometric inequalities, we prove non-linear variational formulation to characterize its principal eigenvalue. This characterization turns out be very robust and allows for simple proof Szeg\"o type inequality as well new reformulation Faber-Krahn ...

We show that a well-known asymptotic series for the logarithm of central binomial coefficient is strictly enveloping in sense P\'olya and Szeg\"o, so error incurred truncating same sign as next term, bounded magnitude by term. consider closely related Binet's function, $\ln\Gamma(z+1/2)$, Riemann-Siegel theta make some historical remarks.

We construct a pointwise Boutet de Monvel-Sj\"ostrand parametrix for the Szeg\H{o} kernel of weakly pseudoconvex three dimensional CR manifold finite type assuming range its tangential operator to be closed; thereby extending earlier analysis Christ. This particularly extends Fefferman's boundary asymptotics Bergman domains in $\mathbb{C}^{2}$, agreement with D'Angelo's example. Finally our res...

In this paper, we establishes certain new weighted Young and P?lya-Szeg?-type inequalities involving Marichev-Saigo-Maeda fractional integral operators. Meanwhile, corresponding Cauchy-Schwarz type inequalities, Shisha-Mond Diaz-Metcalf for operators are also obtained. As applications, some estimates Chebyshev-type with two unknown functions presented. The main results of paper more general inc...