We explore the properties of bilinear products for black hole quasinormal modes (QNMs) formulated on hyperboloidal foliations. We find that, although QNM solutions are smooth and finite on future-directed hyperboloids, the integrand of the bilinear form with respect to which the modes are orthogonal is still divergent. This is a result of the reflection (equivalently, $CPT$) transformation required in the definition of the products, which modifies the behavior of the integrand at the boundaries. We present several regularization procedures that yield a finite and well-defined bilinear form. In addition, we examine an alternative definition of the bilinear products that incorporates flux contributions, discussing its advantages and limitations. Finally, we define the QNM excitation factors and coefficients within the hyperboloidal framework in terms of the bilinear products and compute them explicitly for a choice of mode numbers and constant initial data. For concreteness, we work with the QNMs associated with scalar perturbations of the Schwarzschild family of spacetimes.

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• Classical black holes
• General relativity
• Gravitational waves