A kernel-derived orthogonal basis for spectral functions from Euclidean correlators

Spectral functions play a central role in the characterization of a wide range of physical systems, including strongly interacting quantum field theories and many-body systems. Their non-perturbative determination from Euclidean correlation functions constitutes a well-known ill-posed inverse problem and has motivated the development of numerous reconstruction techniques. In this work, we propose a systematic, prior-free framework for representing spectral functions using an orthogonal functional basis derived directly from the kernel of Euclidean two-point correlation functions. We identify a set of lattice-accessible constraints together with the associated basis functions. These functions can be reorganized into an orthogonal basis within which the spectral function may be approximated in a controlled manner. Using several model spectral functions, we demonstrate that the proposed expansion captures global spectral features and reproduces low-energy transport coefficients with good accuracy. While the numerical implementation requires high-precision Euclidean correlator data, the present framework is intended not as a direct reconstruction method, but rather as a tool for extracting robust constraints and overall spectral structures. The approach may therefore serve as a complementary ingredient or preprocessing step for existing spectral reconstruction techniques.