Multidimensional Widder–Arendt Theorem in Locally Convex Spaces

Key Points

• The central aim is to formulate and prove the multidimensional Widder–Arendt theorem.
• Development and proof of the multidimensional Widder–Arendt theorem.
• Establishment of the integrated form for certain functions.
• Consideration of functions with values in sequentially complete locally convex spaces.
• Established results are new for functions even in the scalar-valued context.
• The proposed theorems contribute to the theory of locally convex spaces.