PRESERVASI STRUKTUR SEMI-ANALITIK DI BAWAH OPERATOR INTEGRAL BERPARAMETER

Muhamad Riananda Fadhilah, NIM.: 22104040060 (2026) PRESERVASI STRUKTUR SEMI-ANALITIK DI BAWAH OPERATOR INTEGRAL BERPARAMETER. Skripsi thesis, UIN SUNAN KALIJAGA YOGYAKARTA.

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Abstract

This study investigates the preservation of semi-analytic structure under parameterized integral operators. The study aims to analyze the relationship between kernel regularity and transformed-function properties, the measurability and integrability of transformed functions, and sufficient conditions that guarantee the preservation of semi-analytic structure. This pure mathematical study employs a literature-based and deductive approach grounded in measure theory, Lebesgue integration, function regularity, and semi-analytic function theory. The results show that the measurability of the kernel and input function, together with appropriate integrability conditions, ensures that the transformed function is measurable and integrable. Furthermore, kernel regularity with respect to output variables and parameters, together with suitable domination conditions on its derivatives, guarantees the continuity, differentiability, and real analyticity of the transformed function. In particular, the estimate ∣

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