<p>In this paper, we introduce a generalized integral transform on function space that extends the classical integral transform associated with the Wiener space. We first establish the existence of the proposed transform for a broad class of functionals under suitable assumptions and investigate its fundamental analytical properties. We also investigate several fundamental properties of the transform and derive various relationships between the generalized integral transform and related integral operators. Furthermore, by applying the translation theorem, we establish a generalized Cameron–Storvick type theorem for the proposed integral transform and derive an associated recurrence formula. The generalized integral transform developed in this paper provides a unified framework for studying generalized Wiener integrals and related analytic Feynman integrals. Consequently, the results presented here furnish new analytical tools for investigating function space integrals and their applications in stochastic analysis, quantum mechanics, and mathematical physics.</p>

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A Generalized Integral Transform with Related Topics on Function Space

  • Praveen Agarwal,
  • Hyun Soo Chung

摘要

In this paper, we introduce a generalized integral transform on function space that extends the classical integral transform associated with the Wiener space. We first establish the existence of the proposed transform for a broad class of functionals under suitable assumptions and investigate its fundamental analytical properties. We also investigate several fundamental properties of the transform and derive various relationships between the generalized integral transform and related integral operators. Furthermore, by applying the translation theorem, we establish a generalized Cameron–Storvick type theorem for the proposed integral transform and derive an associated recurrence formula. The generalized integral transform developed in this paper provides a unified framework for studying generalized Wiener integrals and related analytic Feynman integrals. Consequently, the results presented here furnish new analytical tools for investigating function space integrals and their applications in stochastic analysis, quantum mechanics, and mathematical physics.