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Asynchronous Time Series is a multivariate time series where all the channels are observed asynchronously-independently, making the time series extremely sparse when aligning them. We often observe this effect in applications with complex observation processes, such as health care, climate science, and astronomy, to name a few. Because of the asynchronous nature, they pose a significant challenge to deep learning architectures, which presume that the time series presented to them are regularly sampled, fully observed, and aligned with respect to time. This paper proposes a novel framework, that we call Deep Convolutional Set Functions (DCSF), which is highly scalable and memory efficient, for the asynchronous time series classification task. With the recent advancements in deep set learning architectures, we introduce a model that is invariant to the order in which time series' channels are presented to it. We explore convolutional neural networks, which are well researched for the closely related problem-classification of regularly sampled and fully observed time series, for encoding the set elements. We evaluate DCSF for AsTS classification, and online (per time point) AsTS classification. Our extensive experiments on multiple real-world and synthetic datasets verify that the suggested model performs substantially better than a range of state-of-the-art models in terms of accuracy and run time.