Prior to this change, Python UDFs in Flink's DataFrame API did not support Arrow vectorized execution, limiting performance and compatibility with pyarrow compute operations on columnar batches.

The existing Python UDF framework lacked integration with Arrow data structures and did not distinguish between general, pandas, and Arrow UDF types, preventing direct Arrow batch processing and efficient serialization.

Implemented synchronous Arrow vectorized scalar UDFs by extending the Python DataFrame API and Table API to recognize Arrow UDFs, enhanced the calculation splitting and map merging logic, and upgraded the Arrow operator, worker protocol, and coder to handle native Arrow batches while maintaining pandas defaults. Added support for nested and whole-row arguments, result normalization, and schema validation, along with comprehensive testing across Python and Java components.

Integrating Arrow vectorized UDFs into Flink's Python API significantly improves UDF execution efficiency and compatibility with pyarrow compute operations, demonstrating the value of leveraging native Arrow data structures for high-performance data processing in distributed frameworks.