KUCHLI TEBRANUVCHI INTEGRALLAR OPERATORI UCHUN W2ma,b SOBOLEV FAZOSIDA SARD MA'NOSIDAGI OPTIMAL HERMIT KVADRATURALARI

Abstract. This paper addresses the construction of optimal Hermite quadrature formulas incorporating higher-order derivatives within the Sobolev space for the numerical evaluation of highly oscillatory integral operators. Based on Sard's variational principles and the Riesz representation theorem, the extremal function and the minimal norm of the linear error functional are explicitly derived. A sharp asymptotic error bound characterizing the convergence rate as the frequency is established.